Question

In a triangle with sides a, b, and c, a semicircle touching the sides AC and CB is inscribed whose diameter lies on AB. Then, the radius of the semicircle is

• A. a/2
• B. $\Delta /s$
• C. $\frac{2\Delta }{a+b}$
• D. $\frac{2abc}{\left(s\right)(a+b)}cos\frac{A}{2}cos\frac{B}{2}cos\frac{C}{2}$

Answer 1

The correct option is C $\frac{2\Delta }{a+b}$

$given$
$BC=a,AB=b,AC=c$
$intriangleABC$
$Area=AOC+COB$
$=\frac{1}{2}\times b\times r+\frac{1}{2}\times a\times r$
$=\frac{1}{2}(b\times r+b\times a)$
$=\frac{2\Delta }{a+b}$