Question

In the given fig,AB is a tangent to a circle with center o .prove angle BPQ =angle PRQ

Answer 1

Answer:

Step-by-step explanation:

∠PQR=90° (Angle in the semi circle is right angle)

Also,from triangle PQR, we have

∠RPQ+∠PQR+∠PRQ=180° (angle sum property)

∠RPQ+90°+∠PRQ=180°

∠RPQ=90°-∠PRQ                                                             (1)

Also, ∠BPR=90°(angle made on the tangent)               (2)

Now, ∠BPR=∠RPQ+∠QPB

90°=∠RPQ+∠QPB

From (1), we get

90°=90°-∠PRQ+∠QPB

∠QPB=∠PRQ

Hence proved.

Answer 2

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