SSC CGL 18 Aug 2021 Shift 2 Paper

Question : 70 of 100

Marks: +1, -0

A B

is a chord of a circle in minor segment with centre

O . C

is a point on the minor arc of the circle between the points

A

and

B

. The tangents to the circle at

A

and

B

meet at the point

P

. If

∠ A C B=102^{∘}

, then what is the measure of

∠ A P B

Solution:

Given,

∠ A C B=102^{∘}

We know that,

\;∠ A C B=90^{∘}+\;{∠ P}/{2}

⇒\;90^{∘}+\;{∠ P}/{2}=102^{∘}

⇒\;\;{∠ P}/{2}=102^{∘}-90^{∘}=12^{∘}

∴ \;∠ A P B=24^{∘}

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