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In Delta ABC, right angled at A, cos^(-1...

In `Delta ABC`, right angled at A, `cos^(-1)((R )/(r_(2)+r_(3)))` is

A

`30^(@)`

B

`60^(@)`

C

`90^(@)`

D

`45^(@)`

Text Solution

Verified by Experts

The correct Answer is:
B
`r_(2)+r_(3)=4R"cos"^(2)(A)/(2)`
`angle A=90^(@)`
`therefore cos^(-1)((R )/(r_(2)+r_(3)))`
`=cos^(-1)((R )/(4"R cos"^(2)(A)/(2)))`
`="cos"^(-1)(1)/(2)`
`=60^(@)`
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