Question

In the figure below P,Q,R are the points where the incircle of $△ABC$ touches the sides

$\angle AQR$ and $\angle ARQ$ are ______ , ______ respectively.

• A. ${40}^{\circ },{70}^{\circ }$
• B. ${60}^{\circ },{60}^{\circ }$
• C. ${50}^{\circ },{40}^{\circ }$
• D. ${70}^{\circ },{140}^{\circ }$

Answer 1

The correct option is B

${60}^{\circ },{60}^{\circ }$

,AQ = AR (tangents from same point)

So,$\angle AQR=\angle ARQ$

=$\frac{180-40}{2}={60}^{\circ }$

$\angle AQR=\angle ARQ={60}^{\circ }$