PSAT Math Multiple-Choice Question 82: Answer and Explanation

Question: 82

A circle with center O has diameter AB. Segment AC is tangent to the circle at point A and has a length of 5. If the area of the circle is 36π, what is the perimeter of triangle ABC?

• A. 15
• B. 25
• C. 30
• D. 60

Correct Answer: C

Explanation:

C

The question asks for the perimeter of triangle ABC. Since no figure is provided, start by drawing the figure according to the description in the question. The figure should look like the following:

Next, write down the equations needed to answer the question. Since the area of the circle is 36π, and the formula is A = πr², the radius of the circle is 6. Therefore, the diameter of the circle is 12. Since a line that is tangent to a circle forms a 90° angle with the radius at the point of tangency, the side lengths of this right triangle are a 5–12-13 Pythagorean triple. To find the perimeter of the triangle, add the side lengths to get 5 + 12 + 13 = 30. The correct answer is (C).