Solveeit Logo
Login

Question

Question: In a DABC, r<sup>2</sup> + r<sub>1</sub><sup>2</sup>+ r<sub>2</sub><sup>2</sup> + r<sub>3</sub><sup>...

In a DABC, r2 + r12+ r22 + r32 + a2 + b2 + c2 is equal to

A

4R2

B

8R2

C

16R2

D

None of these

Answer

16R2

Explanation

Solution

r2 + r12 + r22 + r32 +a2 + b2 + c2

= r2 + (r1 + r2 + r3)2 –2Sr1r2 +(a + b + c)2 – 2ab

= r2 + (4R + r)2 –2s2 + 4s2 –2Sab

= 2r2 + 16R2 + 8rR + 2s2 –2Sab

= 16R2 + 2+ + 2s2 –2Sab

use D = s(s−a)(s−b)(s−c)\sqrt { s ( s - a ) ( s - b ) ( s - c ) } & R =