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  • 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<div class='q

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

Option: 1

\frac{a}{2}
 


Option: 2

\frac{\Delta}{s}
 


Option: 3

\frac{2 \Delta}{a+b}
 


Option: 4

None of these


Answers (1)

best_answer

 Let P be the centre of semicircle.


Then, \operatorname{area}(\triangle A B C)=\Delta
\begin{array}{lr} \Rightarrow & \Delta=\operatorname{area}(\triangle P B C)+\operatorname{area}(\triangle A P C) \\ & \Delta=\frac{1}{2} a \cdot r+\frac{1}{2} b \cdot r \Rightarrow r=\frac{2 \Delta}{a+b} \end{array}

Posted by

Devendra Khairwa

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