# Practice Math Challenge Questions for Third Year ( Geometry ) Part 1

Direction: All answers must be exact. Use pi as pi.    Time: 1 hour

1. The supplement of the complement of an angle is 142°. Find the angle.
2. Two sides of a triangle are 10 and 12. How many different triangles can be made out of these sides?
3. In parallelogram ABCD, AB//CD, AD//BC. AB=(2x-5) cm, BC= (3x-11) cm, AD= (2x-1) cm. How long is CD?
4. ABCD is a cyclic quadrilateral. The measure of angle A is three times the measure of angle C. Find the measure of angle A.
5. ABC is right angle at B and inscribed at circle O. AB=3 cm, BC= 4 cm, What is the area of circle O?
6. The diagonal of a square measures 4 cm, what is the perimeter of the square?
7. The sum of interior angle of a regular polygon is 1260°. How many sides the polygon has?
8. What are the maximum points of intersection if we have 6 lines?
9. The number of diagonals of a regular polygon is 35. How many sides the polygon has?
10. ABCD is a square with an area of 100 cm2. E is the midpoint of AB. What is the area of triangle DEC?
11. The surface area of a sphere is 144pi cm2. What is the volume of the sphere?
12. The measure of the base angle of an isosceles triangle is twice measure of the vertex angle. What is the measure of the vertex angle?
13. Find the area of an equilateral triangle if it altitude is 10 cm?
14. Solve for x:  2: 8-x = 4:9
15. The ratio of the areas of two similar pentagons is 25:49. If the perimeter of the smaller pentagon is 25 cm, what is the perimeter of the larger pentagon?
16. ABCD is a right trapezoid with AB//CD. Angle A=angle D= 90°, angle C= 30°.AB= 6 cm, CD= 10 cm. What is the area of trapezoid?
17. ABCD is a square. A smaller square is drawn by connecting the midpoints of the larger square. What is the ratio of the area of smaller square to the larger square?
18. A secant PAB is intersects the circle O at A and B such that PA>PB. PT is a tangent line to the same circle such that PT= 2PB, PA=8. How long is PT?
19. What is the equation of the line through (2,1) and parallel to 3x-2y-6=0?
20. What is the circumference of a circle with an area of 20pi cm?
21. In parallelogram ABCD, AC meets BD at O. Suppose OA= 3x-2,  OC= 13-6x, OB = 3x+2, find OD.
22. The ratio of the angle of quadrilateral is 2:3:4:6. Find the measure of the smallest angle.
23. Circles O1 and O2 are externally tangent at point P, and have radii 2 cm and 4 cm, respectively. Points A and B, both different from P, are chosen on O1 and O2 respectively, such that A,P, and B are collinear. If AB=4cm, How long is PB?
24. Find the volume of a cube with a diagonal of 24 cm.
25. Find the area of a circle inscribed in a square with an area of 64 cm2

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### 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.