Question

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

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

• A. ${50}^{\circ }$
• B. ${80}^{\circ }$
• C. ${70}^{\circ }$
• D. ${35}^{\circ }$

Answer 1

The correct option is C

${70}^{\circ }$

Join IQ and IR.

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

$\angle QIR$ = ${180}^{\circ }$ - ${40}^{\circ }$ = ${140}^{\circ }$ ..........(Sum of angles of a quadrilateral)

$\angle QPR$ = $\frac{1}{2}\angle QIR$ = $\frac{1}{2}\times {140}^{\circ }$ = ${70}^{\circ }$ ........(Angles at the circumference is half the angle at the centre)