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Two tangents from P to a circle of radius 5 cm are inclined to each other at 60°. How far is P from the centre?

Class 10Tangent Lengths and IncirclesGeometry

A5 cm
B $103 c m$
C10 cm
D $53 c m$

Step-by-Step Solution

OP

bisects ∠APB, so ∠

OP A = 30

°. In right triangle

O A P : sin 30° = \frac{O A}{OP}

, so

OP = 5 \div \frac{1}{2} = 10

cm.

53

cm is the tangent length

P A

.

Answer: C) 10 cm

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