The diagram above is a circle with centre C. P, Q and S are points on the circumference. PS and SR are tangents to the circle. ∠PSR = 36o. Find ∠PQR
720
360
1440
540
Correct answer is A
From ∆PSR
|PS| = |SR| (If two tangents are drawn from an external point of the circle, then they are of equal lengths)
∴ ∆PSR is isosceles
∠PSR + ∠SRP + ∠SPR = 180o (sum of angles in a triangle)
Since |PS| = |SR|; ∠SRP = ∠SPR
⇒ ∠PSR + ∠SRP + ∠SRP = 180o
∠PSR + 2∠SRP = 180o
36o + 2∠SRP = 180o
2∠SRP = 180o - 36o
2∠SRP = 144o
∠SRP = 144o2=720
∠SRP = ∠PQR (angle formed by a tangent and chord is equal to the angle in the alternate segment)
∴ ∠PQR = 720
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