CBSE Class 10 Maths (Standard) 2016 · Paper 30/2/1 · Question 7

Circles 2 marks Medium

In Fig.

2

, from a point

P

, two tangents

P T

and

P S

are drawn to a circle with centre

O

such that

∠ S P T = 12 0^{\circ}

. Prove that

O P = 2 P S

Two tangents PT and PS from external point P to a circle with centre O, with angle SPT = 120 degrees (Fig. 2).

Answer

Since

cos 6 0^{\circ} = \frac{P S}{O P} = \frac{1}{2}

, it follows that

O P = 2 P S

. Hence proved.

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