Question

In the given figure, O is the centre of a circle; PQL adn PRM are the tangents at the points Q and R respectively and S is a point on the circle such that $\angle$ SQL = ${50}^o$ and $\angle$ SRM = ${60}^o$ Then, $\angle$ QSR = ?

(a) ${40}^o$ (b) ${50}^o$ (c) ${60}^o$ (d) ${70}^o$

Answer 1

Join Q to R
<QSR = <SQL = 50 degrees
<RQS = <MRS = 60 degrees
Angle between a chord and a tangent equals the angle subtended by the chord at the circumference in the segment opposite the angle

∴ <QSR = 180 - (60+50) = 70 Degrees (Angles of a triangle add up to 180 degrees)





Here ∠OSQ = ∠OQS = 90° - 50° = 40° and ∠RSQ = ∠SRO = 90° - 60° = 30° .

∴∠QSR = 40° + 30° = 70°.