Question

In a triangle ABC, the incircle (centre O) touches BC, CA and AB at points P, Q and R respectively. Calculate:

i)`∠`QPR .

Answer 1

The incircle touches the sides of the triangle ABC and
OP ⊥ BC,OQ ⊥ AC,OR ⊥ AB

i) Now arc RQ subtends`∠`QOR at the centre and `∠`QPR at the remaining part of the circle. 

∴ `∠`QPR = `1/2` `∠` QOR

⇒ `∠`QPR = `1/2 xx120°`

⇒ `∠` QPR = 60°