Ellipse's Circular Tangents

Geometry Level 5

Inside an ellipse, two circles are drawn which touch the minor axis of the ellipse and also touch the ellipse at the ends of latus rectum. The combined area of the two circles is A1A_1 and area of ellipse is A2A_2.

If A1A2=ab+c where a,b,cN and gcd(a,b,c)=1\displaystyle \frac{A_1}{A_2} = \frac{a}{\sqrt{b} + c} \text{ where } a, b, c \in \N \text{ and } \gcd(a,b,c) = 1, enter answer as a2+b2+c2a^2 + b^2 + c^2.

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