in the given figure, PQ and PR are the tangents to the circle with centre Om RS and QS are the chords of the circle. If the difference between the measures of angle RSQ and angle ROQ is 67 degree, then find the measure of angle RPQ
Answers
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 ∠ROB 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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