If O is centre of a circle and Chord PQ makes an angle 50° with the tangent PR at the point of contact P, then the angle subtended by the chord at the centre is (a) 130° (b) 100° (c) 50° (d) 30° Thus,
∠RPQ + ∠QPO = 90°
∠50 ° + ∠QPO = 90°
∴ ∠QPO = 40°
Also,
Since OP = OQ
∴ ∠QPO = ∠PQO
So, ∠QPO = ∠PQO = 40°
In △P𝑂𝑄
∠QPO + ∠POQ + ∠PQO = 180°
40° + ∠POQ + 40 ° = 180°
∠POQ = 180° – 80°
∠POQ = 100°
So, the correct answer is (b)
Made by
Davneet Singh
Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo
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