COMC COMC Geometry and Combinatorics

Question 1

What is the area of a triangle with vertices at (0, 0), (4, 0), and (0, 3)?

Accepted Answer

6

Answer

12

Answer

7

Answer

10

Question 2

A chord is 4 units from the center of a circle with radius 5. What is the length of the chord?

Accepted Answer

6

Answer

3

Answer

8

Answer

4

Question 3

Two angles of a triangle measure 45° and 75°. What is the measure of the third angle?

Accepted Answer

60°

Answer

50°

Answer

70°

Answer

80°

Question 4

In a right triangle, one leg is 7 and the hypotenuse is 25. What is the length of the other leg?

Accepted Answer

24

Answer

18

Answer

20

Answer

16

Question 5

Two similar triangles have corresponding sides in the ratio 3:5. What is the ratio of their areas?

Accepted Answer

9:25

Answer

3:5

Answer

6:10

Answer

27:125

Question 6

What is the area of a regular hexagon with side length 2?

Accepted Answer

6√3

Answer

4√3

Answer

8√3

Answer

12