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Standard IX

Mathematics

Angle Subtended by Diameter on the Circle

In figure, PQ...

Question

In figure, PQ and PR are tangents to the circle with center O and S is a point on the circle such that $∠$ SQL =50 degree and $∠ S R M$ =60 degree. Find $∠$ QSR.

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Solution

Here $∠ O S Q = ∠ O Q S = 90^{o} - 50^{o} = 40^{o}$ and $∠ R S Q = ∠ S R O = 90^{o} - 60^{o} = 30^{o}$ .
$∠ Q S R = 40^{o} + 30^{o} = 70^{o}$ .

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In figure, PQ and PR are tangents to the circle with center O and S is a point on the circle such that ∠SQL =50 degree and ∠SRM =60 degree. Find ∠QSR.

Here ∠OSQ=∠OQS=90o−50o=40o and∠RSQ=∠SRO=90o−60o=30o.∠QSR=40o+30o=70o.

In figure, PQ and PR are tangents to the circle with center O and S is a point on the circle such that $∠$ SQL =50 degree and $∠ S R M$ =60 degree. Find $∠$ QSR.

Here $∠ O S Q = ∠ O Q S = 90^{o} - 50^{o} = 40^{o}$ and $∠ R S Q = ∠ S R O = 90^{o} - 60^{o} = 30^{o}$ .
$∠ Q S R = 40^{o} + 30^{o} = 70^{o}$ .