Question

In the given figure, O is the centre of incircle for ∆ PQR. Find ∠QOR if ∠QPR = 40°.​

Answer 1

Question:-

In the given figure, O is the centre of incircle for ∆ PQR. Find ∠QOR if ∠QPR = 40°.

Solution:-

PO is joined.

Since the circle is the incircle for ∆ ABC,PO,QO,RO are the angle bisector of ∠P,∠Q and ∠R respectively.

∠CPO = ∠APO

= 1/2 × 40° = 20°

Also, OA⊥PR, OC⊥PQ, OB⊥QR (Radii ⊥ tangent at point of constant).

⇒ ∠OAP = 90°

⇒ ∠AOP = y = 180° – (90° + 20°) = 70°

Now, y + y + x + x + z + z = 360°

⇒ 2y + 2 (x + z) = 360°

⇒ 2(x + z) = 360° – 2y = 360° – 140° = 220°

⇒ x + 2 = 110°

⇒ ∠QOR = 110°

Answer:-

Hence, the value of ∠QOR = 110°.

[Refer Above attachment for the diagram].