Question

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

Using the information given , $\angle RQP$ = ____

• A. ${60}^{\circ }$
• B. ${70}^{\circ }$
• C. ${50}^{\circ }$
• D. ${45}^{\circ }$

Answer 1

The correct option is A

${60}^{\circ }$

Join IP and IR.

$\angle IRB$ = $\angle IPB$ = ${90}^{\circ }$ ...........(Tangent is perpendicular to the radius at the point of contact)

$\angle RIP$ = ${180}^{\circ }$ - ${60}^{\circ }$ = ${120}^{\circ }$ ..........(Sum of angles of a quadrilateral)

$\angle RQP$ = $\frac{1}{2}\angle RIP$ = $\frac{1}{2}\times {120}^{\circ }$ = ${60}^{\circ }$ ........(Angles at the circumference is half the angle at the centre)