Question

In the given fig.,PQL and PRM are tangents to the circle with centre O at the points Q and R, respectively.If S is a point on a circle such that ∠SQL=50° and ∠SRM=60°,then find the value of ∠QSR.

Answer 1

Answer:

<QSR = 70°

Step-by-step explanation:

i) Given <SRM = 60°

<SRM + <SRO = 90°

/* tangent , radius relation */

=> 60° + <SRO = 90°

=> <SRO = 90° - 60° = 30°

ii) In ∆OSR ,

OS = OR ( radii of same circle )

=> <OSR = <SRO = 30°

/* Angles opposite to equal sides are equal */

Similarly ,

iii ) Given <SQL = 50°,

<SQO = 90° - <SQL

= 90° - 50°

= 40°

iv ) In ∆OSQ,

OS = OQ

=> <OSQ = <SQO = 40°--(2)

v) <QSR = <OSR+<OSQ

= 30° + 40°

= 70°

•••♪

Answer 2

Answer:

theorem used

1) the tangents to a circle is perpendicular tobthe radius through the point of contact

2) angle opp. to equal sides equal

3) angle sum property of a circle

question from class 10 CBSE - CIRCLES