Question

In an isosceles triangle with base angle $\alpha$ and lateral side b, $Rr=$

• A. $\frac{b^2\cos \alpha }{2(1-\cos \alpha )}$
• B. $\frac{b\cos \alpha }{2(1-\cos \alpha )}$
• C. $\frac{b^2\cos \alpha }{2(1+\cos \alpha )}$
• D. $\frac{b\cos \alpha }{2(1+\cos \alpha )}$

Answer 1

The correct option is C $\frac{b^2\cos \alpha }{2(1+\cos \alpha )}$

$Rr=\frac{abc}{4\Delta }\times \frac{\Delta }{s}=\frac{abc}{2(a+b+c)}$

$=\frac{b\cdot b\cdot 2b\cos \alpha }{2(b+b+2b\cos \alpha )}=\frac{b^2\cos \alpha }{2(1+\cos \alpha )}$