A $3-4-5$ 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 $B$?

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Circle Inscribed Diameter: The diameter of a circle inscribed in a right triangle is equal to the hypotenuse of the triangle. For circle A, the hypotenuse of the $3-4-5$ triangle is 5, which is the diameter of circle A. For circle B, the hypotenuse of the $5-12-13$ triangle is 13, which is the diameter of circle B.Radius Calculation: The radius of circle A is half of its diameter, so the radius of circle A is $5/2$. The radius of circle B is half of its diameter, so the radius of circle B is $13/2$.Area Calculation: The area of a circle is given by the formula $A = \pi r^2$. The area of circle A is $\pi (5/2)^2$ and the area of circle B is $\pi (13/2)^2$.Area Simplification: Simplify the areas:  Area of circle A is $\pi (25/4)$ and  Area of circle B is $\pi (169/4)$.Area Ratio Calculation: To find the ratio of the area of circle A to the area of circle B, divide the area of circle A by the area of circle B:  $\frac{\pi (25/4)}{\pi (169/4)}$.Final Ratio: The $\pi$ terms cancel out and the ratio simplifies to $\frac{25/4}{169/4}$. This further simplifies to $\frac{25}{169}$ when the common denominator of 4 is canceled out.

A $3-4-5$ 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 $B$ ?

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A $3-4-5$ 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 $B$ ?