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

(a) 140° 

(b) 110° 

(c) 80° 

(d) 120°

1 Answer

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by (22.8k points)
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Best answer

Answer : (b) 110º 

PO is joined.

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

∠CPO = ∠APO

= \(\frac{1}{2}\)× 40° = 20° 

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

⇒ ∠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 + z = 110° 

⇒ ∠QOR = 110°

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