# Facts About Cyclic Quadrilateral

Cyclic quadrilateral is a special kind of quadrilateral inscribed in a circle. Inscribe means that the vertices of quadrilateral are on the circumference of the circle. A square, rectangle, isosceles trapezoid are some of cyclic quadrilaterals. Below are the some facts about this special figure.

1. The opposite angle of cyclic quadrilateral is supplementary.

°

°

2. Ptolemy’s Theorem. This theorem is a special case of Ptolemy’s Inequality. He formulated the following equation relating the sides and diagonals.

3. Diagonals as Cords. Using the basic theorem in geometry, we can relate the diagonals with respect to their intersections as follows.

4. Brahmagupta’s Formula. Brahmagupta of India derived a formula to find the area of cyclic quadrilateral.

Where S is the semiperimeter

Use the facts above to solve for the following problems.

**Problem 1:** In a cyclic quadrilateral , If °. Find the measure of

Solution:

Using the first fact, opposite angles are supplementary.

°

°°

°

°

**Problem 2: **In cyclic quadrilateral , °. If , and two opposite sides have length 2 and 3. What is the area of quadrilateral?

Solution:

Draft the quadrilateral as follows,

Since and are right triangle and is the hypotenuse of both triangles, we can find sides and by Pythagorean Theorem.

The area can be found using Brahmagupta’s formula or using the fact that both triangles are right triangle.

sq. units

** **

### Dan

#### Latest posts by Dan (see all)

- 2016 MMC Schedule - November 4, 2015
- 2014 MTAP reviewer for Grade 3 - September 30, 2015
- 2015 MTAP reviewer for 4th year solution part 1 - August 22, 2015

I like what you dudes are now up to. This sort of cool work and coverage! Keep up the great work guys, I’ve included you our blogroll.

Great website you have here but I was curious about if you knew of any forums that cover the same topics talked about in this article? I’d really love to be a part of community where I can get comments from other knowledgeable people that share the same interest. If you have any suggestions, please let me know. Bless you!

GNM54x This is very interesting, You are a very skilled blogger. I have joined your rss feed and look forward to seeking more of your wonderful post. Also, I ave shared your web site in my social networks!

wIRAKC Really informative article. Much obliged.

801509 751757This internet website is often a walk-through rather than the details you wanted about it and didnt know who ought to. Glimpse here, and youll definitely discover it. 378161

844007 188477These kinds of Search marketing boxes normally realistic, healthy and balanced as a result receive just about every customer service necessary for some product. Link Building Services 329182

Hi,I log on to your new stuff named “Facts About Cyclic Quadrilateral – Techie Math Teacher” like every week.Your story-telling style is witty, keep it up! And you can look our website about proxy server list.

lace frontal https://www.youtube.com/watch?v=ny8rUpI_98I're genuinely cute and fashion. I purchased the one particular and love them.

Way cool! Some extremely valid points! I appreciate you penning this write-up plus the rest of the site is very good.