2023 AMC 10B Problems/Problem 3
Revision as of 15:52, 15 November 2023 by Mintylemon66 (talk | contribs)
Problem
A right triangle is inscribed in circle
, and a
right triangle is inscribed in circle
. What is the ratio of the area of circle
to the area of circle
?
Solution
Since the arc angle of the diameter of a circle is degrees, the hypotenuse of each these two triangles is respectively the diameter of circles
and
.
Therefore the ratio of the areas equals the radius of circle squared : the radius of circle
squared
the diameter of circle
, squared :
the diameter of circle
, squared
the diameter of circle
, squared: the diameter of circle
, squared
$=\boxed{\textbf{(B) }\dfrac{25}{169}.$ (Error compiling LaTeX. Unknown error_msg)
~Mintylemon66