Question

(c) In the given figure, PQ = QR, angle RQP= 66°, PC and CQ are tangents to the
circle with centre O. Calculate the values of (i) angle QOP, and (ii) angle QCP.

.fig is given above​
wrong answer is strictly not allowed

Answer 1

Answer:

QOP = 94, QCP = 86

Step-by-step explanation:

PQ = QR

Thus, ∠P = ∠R

Also, ∠P + ∠Q + ∠R = 180  ( angle sum )

       ∠Q = 86

Thus, 2 ∠P = 180 - 86 =94

thus ∠P = 47 = ∠R

∠CQP = ∠QRP ( alternate segment theorem  since  CQ is tangent to circle )

Thus ∠CQP = 47 = ∠CPQ ( SInce CP=CQ, tangent segment theorem )

Thus, in triangle CPQ, ∠C + ∠P + ∠Q = 180  

Thus, ∠C = 180 - 2 * 47 = 180 - 94 = 86

Thus in Quad OPCQ, ∠P + ∠Q = 180 ( Tangent are perpendicular to radius)

Hence it is cyclic

Thus ∠O + ∠C = 180

That is ∠O = 180 - 86 = 94