AIME Geometry 1 — Questions and Answers
Question 1: A circle has center (3, -1) and passes through (7, -1). What is its area?
- 16π (Correct answer)
- 8π
- 4π
- 12π
Correct answer: 16π
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?
- 13 (Correct answer)
- 17
- 11
- 15
Correct answer: 13
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?
- 115° (Correct answer)
- 65°
- 125°
- 55°
Correct answer: 115°
Co-interior angles are supplementary, so 180°-65°=115°.
Question 4: A rectangle has perimeter 36 and width 6. What is its area?
- 72 (Correct answer)
- 54
- 90
- 36
Correct answer: 72
Length=(36-12)/2=12; area=12×6=72.
Question 5: What is the area of an equilateral triangle with side length 4?
- 4√3 (Correct answer)
- 8√3
- 2√3
- 16√3
Correct answer: 4√3
Area = (√3/4)×4^2=(√3/4)×16=4√3.
Question 6: A sector of a circle has radius 6 and central angle 60°. What is the arc length?
- 2π (Correct answer)
- π
- 3π
- 6π
Correct answer: 2π
Arc length = (60/360)×2π×6=2π.
AIME Geometry 1
A circle has center (3, -1) and passes through (7, -1).
What is its area?