AIME Geometry

Question 1

A circle has center (3, -1) and passes through (7, -1). What is its area?

Accepted Answer

16π

Answer

The radius is the distance from center to point: |7-3|=4, so area=π(4)^2=16π.

Question 2

In a right triangle with legs 5 and 12, what is the length of the hypotenuse?

Accepted Answer

13

Answer

By the Pythagorean theorem, √(25+144)=√169=13.

Question 3

Two parallel lines are cut by a transversal. If one interior angle is 65°, what is the co-interior (same-side interior) angle?

Accepted Answer

115°

Answer

Co-interior angles are supplementary, so 180°-65°=115°.

Question 4

A rectangle has perimeter 36 and width 6. What is its area?

Accepted Answer

72

Answer

Length=(36-12)/2=12; area=12×6=72.

Question 5

What is the area of an equilateral triangle with side length 4?

Accepted Answer

4√3

Answer

Area = (√3/4)×4^2=(√3/4)×16=4√3.

AIME - American Invitational Mathematics Examination Practice Test