AMC12 Geometry 1 — Questions and Answers
Question 1: A circle has area 16pi. What is its circumference?
- 4pi
- 16pi
- 2pi
- 8pi (Correct answer)
Correct answer: 8pi
From pi*r^2=16pi we get r=4, so C=2pi(4)=8pi.
Question 2: In right triangle ABC with right angle at B, AB=5 and BC=12. What is sin(A)?
- 5/13
- 5/12
- 12/5
- 12/13 (Correct answer)
Correct answer: 12/13
The hypotenuse AC=13, and sin(A)=BC/AC=12/13.
Question 3: The diagonals of a rhombus are 6 and 8. What is its side length?
- 7
- 10
- 4
- 5 (Correct answer)
Correct answer: 5
The half-diagonals are 3 and 4; side=sqrt(9+16)=5.
Question 4: A rectangle has perimeter 34 and area 60. What is the length of its diagonal?
- 15
- 11
- 17
- 13 (Correct answer)
Correct answer: 13
l+w=17 and lw=60 gives l=12,w=5; diagonal=sqrt(144+25)=13.
Question 5: What is the area of an equilateral triangle with side length 4?
- 8sqrt(3)
- 2sqrt(3)
- 16sqrt(3)
- 4sqrt(3) (Correct answer)
Correct answer: 4sqrt(3)
Area=(sqrt(3)/4)*s^2=(sqrt(3)/4)*16=4sqrt(3).
Question 6: Two circles of radius 3 and 5 are externally tangent. What is the distance between their centers?
- 2
- 15
- 4
- 8 (Correct answer)
Correct answer: 8
For externally tangent circles, center-to-center distance=r1+r2=3+5=8.
AMC12 Geometry 1
A circle has area 16pi.
What is its circumference?