23. In the given figure, PQ and PR are the tangents to the circle with centre 'O'. RS and QS are the chords of the
circle. If the difference between the measures of AngleRSQ and AngleROQ is 67°, then find the measure of AngleRPQ.
Answers
Answer:
happy Lori bro
Given : PQ and PR are the tangents to the circle with centre 'O'. RS and QS are the chords of the circle.
difference between the measures of ∠RSQ and ∠ROQ is 67°
To Find : measure of ∠RPQ
Solution:
∠ROQ = 2 ∠RSQ ( angle by same arc RQ at center and remaining arc circle )
difference between the measures of ∠RSQ and ∠ROQ is 67°,
∠ROQ - ∠RSQ = 67°
=> 2 ∠RSQ - ∠RSQ = 67°
=> ∠RSQ = 67°
∠ROQ = 2 ∠RSQ
=> ∠ROQ = 2 (67°)
=> ∠ROQ =134°
∠PRO = ∠PQO = 90° as PQ & PR are Tangents
in quadrilateral PQOR
∠PRO + ∠ROQ + ∠PQO + ∠RPQ = 360°
=> 90° + 134° + 90° + ∠RPQ = 360°
=> ∠RPQ = 46°
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