Difference between revisions of "2023 AMC 10B Problems/Problem 3"
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Therefore the ratio of the areas equals the radius of circle <math>A</math> squared : the radius of circle <math>B</math> squared | Therefore the ratio of the areas equals the radius of circle <math>A</math> squared : the radius of circle <math>B</math> squared | ||
<math>=</math> <math>0.5\times</math> the diameter of circle <math>A</math>, squared : <math>0.5\times</math> the diameter of circle <math>B</math>, squared | <math>=</math> <math>0.5\times</math> the diameter of circle <math>A</math>, squared : <math>0.5\times</math> the diameter of circle <math>B</math>, squared | ||
− | <math>=</math> the diameter of circle <math>A</math>, squared: the diameter of circle <math>B</math>, squared | + | <math>=</math> the diameter of circle <math>A</math>, squared: the diameter of circle <math>B</math>, squared <math>=\boxed{\textbf{(B) }\frac{25}{169}}.</math> |
− | <math>=\boxed{\textbf{(B) }\ | ||
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~Mintylemon66 | ~Mintylemon66 |
Revision as of 15:55, 15 November 2023
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
~Mintylemon66