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In triangle A B C ,b^2sin2C+c^2sin2B=2bc...

In triangle `A B C ,b^2sin2C+c^2sin2B=2bc where b=20 ,c=21 ,` then inradius= (a) 4 (b) 6 (c) 8 (d) 9

A

4

B

6

C

8

D

9

Text Solution

Verified by Experts

The correct Answer is:
B
`b^(2) sin 2C + c^(2) sin 2B = 2bc`
`rArr b^(2) (2 sin C cos C) + c^(2) (2 sin B cos B) = 2bc`
`rArr b^(2) (c cos C) + c^(2) (b cos B) = 2Rbc`
`rArr b cos C + c cos B = 2R`
`rArr a = 2R`
`rArr A = 90^(@)`
`:. a^(2) = b^(2) + c^(2) = 400 + 441 = 841`
`rarr a = 29`
Now, `r = (2Delta)/(2s) = (20 xx 21)/(20 + 21 + 29) = (20 xx 21)/(70) = 6`
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