Question

In a $\Delta ABC,$ a semicircle is inscribed, whose diameter lies on the side c. Then the radius of the semicircle is (Where $\Delta$ is the area of the triangle ABC)

• A. $\frac{2\Delta }{a+b}$
• B. $\frac{2\Delta }{a+b-c}$
• C. $\frac{2\Delta }{s}$
• D. $\frac{c}{2}$

Answer 1

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

given $BC=a,AB=b,AC=c$

$△$ is the area of triangle

Area of triangle $△$ABC = ($△$AOC+$△$COB)

Area of triangle

$△=\frac{1}{2}\times b\times r+\frac{1}{2}a\times r$

$△=\frac{1}{2}(b\times r+a\times r)$

$\frac{2△}{a+b}=r$