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If the radius of the circumcircle of a triangle is 10 and that of the incircle is 5, then the square of the sum of radii of the described circles is?

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1225

2025

answer is D.

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Detailed Solution

Given R=10, r = 5
Since,

r_{1} + r_{2} + r_{3} = 4 R + r = 4 \times 10 + 5 = 45

\Rightarrow {(r_{1} + r_{2} + r_{3})}^{2} = 45^{2} = 2025

So, Option 4 is correct.

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