2023 AMC 10B Problem 3

Problem 3 of 25EasierGeometry

3

4

5

right triangle is inscribed in circle

A,

and a

5

12

13

right triangle is inscribed in circle

B.

What is the ratio of the area of circle

A

to the area of circle

B?

Show solution

Solution

The hypotenuse of a right triangle is a diameter of the circle around it. So circle

A

has diameter

5

and circle

B

has diameter

13.

Areas scale as the square of that, giving

\left(\frac{5}{13}\right)^2 = \frac{25}{169}.

Thus, D is the correct answer.

Tagged: circumcircle, circumcenter, and circumradius · right triangle · area ratio