Question

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 escribed circles is

Answer 1

Given $R=10,r=5$

We know that

$r_1+r_2+r_3=4R+r$

$\Rightarrow (r_1+r_2+r_3{)}^2=(4\times 10+5{)}^2=2025$