2023 AMC 12B Problems/Problem 3
Problem
A 3-4-5 right triangle is inscribed circle , and a 5-12-13 right triangle is inscribed in circle
. What is the ratio of the area of circle
to circle
?
Solution 1
Because the triangle are right triangles, we know the hypotenuses are diameters of circles and
. Thus, their radii are 2.5 and 6.5 (respectively). Square the two numbers and multiply
to get
and
as the areas of the circles. Multiply 4 on both numbers to get
and
. Lastly, divide, to get your answer:
$\boxed{\textbf{(D) \frac{25}{169}}}$ (Error compiling LaTeX. Unknown error_msg).
~Failure.net