Incircle and Excircles of right triangle 2

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In a right triangle $ABC$ $C$ = $90^\circ$ . $AB$ = $17$ .Let $a$ , $b$ , $c$ and $d$ denote radius of incircle and three excircles respectively.Find $a^2$ + $b^2$ + $c^2$ + $d^2$

The answer is 578.

1 solution

Rifath Rahman
Feb 5, 2015

First of all $AB$ is hypotenuse.In case of right triangle $a^2$ + $b^2$ + $c^2$ + $d^2$ = $2\times AB^2$ .So, $2 \times AB^2$ = $2\times 17^2$ = $578$

Incircle and Excircles of right triangle 2

The answer is 578.

1 solution

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