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Consider a triangle ABC and let a, b and...

Consider a triangle ABC and let a, b and c denote the lengths of the sides opposite to vertices A, B and C, respectivelu. Suppose `a = 6, b = 10` and the triangle is `15 sqrt3`. If `angle ACB` is obtus and if r denotes than radius of the incircle of the triangle, then the value of `r^(2)` is _____

A

2

B

4

C

3

D

6

Text Solution

Verified by Experts

We have,
Area=`1/2absinC`
`rArr15sqrt3=1/2xx6xx10xx` sinC
`rArrsinC=(sqrt3)/2rArrC=120^(@)`
`thereforec^(2)=a^(2)+b^(2)-2abcosC`
`c^(2)=36+100-120xx(-1/2)=196rArrc=14`
So, 2s = a + b + c `rArr` 2s = 30 `rArr` s = 15
`thereforer=(Delta)/s=(15sqrt3)/15=sqrt3rArrr^(2)=3`
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