# 2013 MTAP Saturday Class Challenge Problem Solution Part 2

Previously, we solved problems 1 to 3 of the MTAP Saturday Class S-5 for 4th year. Now let’s continue the problem solving with the rest of the problems.

Problem 6:

If the length of the common chord intersecting circles is $16$ feet and the radii are $10$ and $17$ feet, find the distance between the centers of the circle.

Solution: Draw  and label the figure as shown below

Since $FG=16, FH=HG=8$

Observe that $\triangle FBH$ and $\triangle FHD$ are right triangles, thus we can use Pythagorean Theorem to solve for $BH$ and $DH$.

Solving for $BH$:

$10^2=8^2+BH^2$

$100=64+BH^2$

$BH^2=100-64=36$

$BH=6$

Solving for $DH$:

$17^2=8^2+DH^2$

$289=64+DH^2$

$DH^2=289-64=225$

$DH=15$

The distance between the circles $BD=BH+DH$

Solving for the distance between two circles we have,

$BD=BH+DH$

$BD=6+15$

$\boxed{BD=21}$

Problem 7:

The shortest distance between from a point to a circle is 6 in. and the greatest distance from the same point to a circle is 24 in. Find the length of the tangent from that point.

Solution: Draw and label the figure accordingly,

In the figure, PA is the shortest distance and PB is the greatest distance. PT is the length of the tangent. We assign it by a variable x.

$AO=OT=OB=9$ since they are all the radii of the circle.

$\triangle PTO$ is a right triangle with right angle at $\angle{PTO}$.

Using Pythagorean Theorem in $\triangle PTO$ we have,

$PO^2=PT^2+OT^2$

$15^2=x^2+9^2$

$x^2=15^2-9^2=144$

$\boxed{x=12 in}$

Problem 8:

From an external point two secants, PAB and PCD, are drawn, one cutting the circle at A and B, the other cutting it at C and D. If PB=27 in., AB= 21 in., and PC=CD. What is the length of PD?

Solution: Draw and label the figure accordingly as shown below

Using the secant-secant theorem,

$PA\cdot PB=PC\cdot PD$

$6\cdot 27=x\cdot 2x$

$2\cdot 9^2=2x^2$

$x^2=9^2$

$x=9$

Since $PD=2PC,PD=2\cdot9=\boxed{18 in}$

### Dan

Blogger and a Math enthusiast. Has no interest in Mathematics until MMC came. Aside from doing math, he also loves to travel and watch movies.

### 126 Responses

1. Sang says:

I was recommended this blog by my cousin. I’m not sure whether this post is written by him as no one else know such detailed about my problem. You’re amazing! Thanks!

2. A formidable share, I simply given this onto a colleague who was doing a little analysis on this. And he in reality purchased me breakfast because I found it for him.. smile. So let me reword that: Thnx for the treat! However yeah Thnkx for spending the time to discuss this, I really feel strongly about it and love studying more on this topic. If possible, as you develop into expertise, would you thoughts updating your weblog with extra details? It is extremely helpful for me. Huge thumb up for this weblog post!

3. 5HLe54 Thanks a lot for the article post.Really looking forward to read more. Cool.

4. vjsRc6 Thanks-a-mundo for the blog.Really looking forward to read more. Really Great.

5. You made some decent points there. I checked on the web for more information about the issue and found most individuals will go along with your views on this web site.

6. A big thank you for your article post.Really thank you! Will read on…

7. Thanks for sharing, this is a fantastic blog.Really looking forward to read more. Much obliged.

8. Really enjoyed this blog article.Really thank you! Want more.

9. reader amused. Between your wit and your videos, I was almost moved to start my own blog (well,

10. I really enjoy the post.Really looking forward to read more. Will read on…

11. Major thanks for the blog.Much thanks again. Really Great.

12. china dealz says:

in that case, because it is the best for the lender to offset the risk involved

13. Wow, wonderful weblog format! How long have you been blogging for? you made running a blog glance easy. The overall glance of your web site is fantastic, let alone the content material!

14. beekeeping says:

Some really select content on this site, saved to bookmarks.

15. UoN says:

Major thankies for the blog post.Really looking forward to read more. Really Great.

16. bbw wife says:

This is really interesting, You are a very skilled blogger. I ave joined your feed and look forward to seeking more of your wonderful post. Also, I have shared your website in my social networks!

17. Im thankful for the article post.Thanks Again. Really Cool.

18. Pretty! This was an incredibly wonderful article. Thank you for providing these details.

19. Major thankies for the post.Thanks Again. Want more.

20. Wow, great blog.Much thanks again. Really Great.

21. Appreciate you sharing, great blog post.Really looking forward to read more. Keep writing.

22. un ton autres ai pris issue a ce, lettre sans meme monde meme profite et quoi tokyo pas va changer que avaient

23. romance understanding. With online video clip clip

24. This web site certainly has all the info I needed concerning this subject and didn at know who to ask.

25. Major thankies for the blog.Really thank you! Really Cool.

26. Therefore that as why this piece of writing is outstdanding.

27. I really like and appreciate your post.Really looking forward to read more. Really Cool.

28. STForex says:

Wow, amazing blog layout! How long have you been blogging for? you make blogging look easy. The overall look of your web site is fantastic, as well as the content!

29. I am so grateful for your post.Really thank you! Will read on…

30. Incredible points. Great arguments. Keep up the good spirit.

31. pretty useful stuff, overall I feel this is really worth a bookmark, thanks

32. friends says:

Very informative blog post. Will read on

33. Photography says:

Great, thanks for sharing this blog post.Really looking forward to read more. Really Cool.

34. Friv says:

their payment approaches. With the introduction of this kind of

35. Very nice post and right to the point. I don at know if this is really the best place to ask but do you people have any thoughts on where to hire some professional writers? Thanks

37. Usually I do not read post on blogs, however I wish to say that this write-up very forced me to take a look at and do it! Your writing style has been surprised me. Thank you, very nice article.

38. Painting says:

Major thankies for the article post. Will read on…

39. Wow, superb blog layout! How long have you been blogging for? you make blogging look easy. The overall look of your website is fantastic, as well as the content!

40. Well I definitely enjoyed studying it. This subject offered by you is very constructive for good planning.

41. your blog is really a walk-through for all of the information you wanted about this and didn at know who to ask. Glimpse here, and you all definitely discover it.

42. law office says:

wow, awesome blog.Much thanks again. Much obliged.

43. You made some good points there. I checked on the web for more info about the issue and found most people will go along with your views on this site.

44. What the amazing post you ave made. I merely stopped into inform you I truly enjoyed the actual read and shall be dropping by from time to time from right now on.

46. It as not that I want to duplicate your website, but I really like the design and style. Could you tell me which theme are you using? Or was it custom made?

47. louis vuitton outlet yorkdale the moment exploring the best tips and hints

48. Wonderful blog! I found it while searching on Yahoo News. Do you have any tips on how to get listed in Yahoo News? I ave been trying for a while but I never seem to get there! Many thanks

49. Buzzinity says:

Nice Site , guys! Good Articles aswell. Bookmarked

50. Really informative blog article.Much thanks again. Great.

51. Wow! Thank you! I continually wanted to write on my blog something like that. Can I take a part of your post to my website?

52. I value the article.Thanks Again.

53. This is one awesome article post.Really looking forward to read more. Keep writing.

54. You ave made some decent points there. I checked on the web to find out more about the issue and found most individuals will go along with your views on this web site.

55. Appreciate you sharing, great blog.Thanks Again. Really Great.

56. Tamara says:

wow, awesome article.Really thank you! Cool.

58. Isa says:

Wow, superb blog layout! How long have you been blogging for? you made blogging look easy. The overall look of your site is magnificent, let alone the content!. Thanks For Your article about sex.

59. Looking forward to reading more. Great blog.

60. This is one awesome article.Thanks Again. Great.

61. Lee says:

Thank you for the good writeup. It in fact was a amusement account it. Look advanced to far added agreeable from you! By the way, how could we communicate?

62. Laid-off says:

Very good blog article. Will read on…

63. This is one awesome blog article.Really looking forward to read more. Really Cool.

64. Womens Ray Ban Sunglasses Womens Ray Ban Sunglasses

65. Thanks again for the article post. Really Great.

66. Music says:

It as hard to find well-informed people for this topic, but you seem like you know what you are talking about! Thanks

67. It as really very complicated in this busy life to listen news on TV, thus I just use internet for that purpose, and take the latest news.

68. Your style is unique in comparison to other folks I have read stuff from. I appreciate you for posting when you have the opportunity, Guess I will just bookmark this blog.

69. soundcloud says:

Really informative article post.Much thanks again.

70. I truly appreciate this post.Really thank you! Cool.

71. Im obliged for the blog post.Really thank you! Really Great.

72. #weed says:

Thanks so much for the article. Will read on…

73. time a comment is added I get four emails with the

74. This site was how do you say it? Relevant!! Finally I ave found something which helped me. Thank you!

75. Pretty! This has been a really wonderful article. Thank you for providing this information.

76. Informative and precise Its difficult to find informative and accurate info but here I found

77. The Silent Shard This can in all probability be very practical for many of one as job opportunities I want to really don at only with my web site but

78. Thank you, I ave just been searching for information about this topic for ages and yours is the greatest I have discovered till now. But, what about the conclusion? Are you sure about the source?

79. Very informative article. You really grabbed my interest with the way you cleverly featured your points. I agree with most of your content and I am analyzing some areas of interest.

80. Simply a smiling visitor here to share the love (:, btw great pattern. аЂаHe profits most who serves best.аЂа by Arthur F. Sheldon.

81. more details says:

82. I appreciate you sharing this blog post.Much thanks again.

83. You have made some good points there. I looked on the internet to learn more about the issue and found most individuals will go along with your views on this site.

84. really very good submit, i basically adore this website, keep on it

86. Really enjoyed this blog.Much thanks again. Keep writing.

87. This piece of writing on the topic of SEO provides clear idea for new SEO people that how to do Search engine optimization, so keep it up. Good work

88. Thanks-a-mundo for the blog article. Much obliged.

89. Thanks for another excellent article. Where else could anyone get that type of info in such an ideal way of writing? I ave a presentation next week, and I am on the look for such information.

90. check out says:

That as a great post. Thank you so much.

91. lushacre.com.sg I want to start a blog but would like to own the domain. Any ideas how to go about this?.

92. pretty useful stuff, overall I consider this is worthy of a bookmark, thanks

93. Past Exhibition CARTApartment CART Apartment CART Blog

94. Your style is so unique in comparison to other people I have read stuff from. Thank you for posting when you have the opportunity, Guess I all just bookmark this page.

95. Wonderful blog! I found it while surfing around on Yahoo News. Do you have any tips on how to get listed in Yahoo News? I ave been trying for a while but I never seem to get there! Thanks

96. Thank you ever so for you article post.Thanks Again. Great.

97. Im obliged for the post.Really thank you! Really Great.

98. I think this is a real great blog article.Much thanks again. Really Cool.

99. I really liked your post.Much thanks again. Want more.

100. It as hard to come by educated people in this particular topic, but you sound like you know what you are talking about! Thanks

101. ebooki.net says:

102. Teresa says:

103. 2017 says:

Wow, amazing blog layout! How long have you been blogging for? you make blogging look easy. The overall look of your website is magnificent, let alone the content!. Thanks For Your article about sex.

104. Very neat post.Much thanks again. Awesome.

105. Really enjoyed this post.Much thanks again. Much obliged.

106. Thank you for some other wonderful post. Where else may just anybody get that type of info in such an ideal way of writing? I have a presentation subsequent week, and I am on the search for such info.

107. Way cool! Some extremely valid points! I appreciate you penning this post and also the rest of the site is extremely good.

108. Very neat blog.Much thanks again. Fantastic.

109. I think one of your current ads caused my internet browser to resize, you might well need to get that on your blacklist.

110. ejuice says:

This is a topic that as close to my heart Best wishes! Exactly where are your contact details though?

111. Sometimes I also see something like this, but earlier I didn`t pay much attention to this!

112. Hey, thanks for the blog. Cool.

113. Looking forward to reading more. Great blog post. Much obliged.

114. E-commerce says:

I cannot thank you enough for the article post.Really looking forward to read more. Really Great.

115. Webdesign says:

like they are coming from brain dead visitors?

116. Major thankies for the post.Really looking forward to read more. Really Great.

Thank you for your blog article. this site

118. I am so grateful for your blog article.Really thank you! Fantastic.

119. Thanks so much for the blog article.

120. Im grateful for the article.Really looking forward to read more. Really Great.

121. Very good article post.Really looking forward to read more. Great.

122. you ave gotten a fantastic blog here! would you prefer to make some invite posts on my weblog?

123. Muchos Gracias for your blog post.Really thank you! Really Great.

124. Wonderful article! We are linking to this great

125. Thank you for the auspicious writeup. It in fact was a amusement account it. Look advanced to more added agreeable from you! By the way, how could we communicate?

126. servers list says:

Im thankful for the blog article.Really looking forward to read more. Really Cool.