CBSE Class 10 Maths (Standard) 2017 · Paper 30(B) · Question 10

Circles 2 marks Medium

If, from an external point

P

of a circle with centre

O

, two tangents

P A

and

P B

are drawn such that

∠ B P A = 12 0^{\circ}

, then show that

O P = 2 P A

Answer

Since

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

, we get

O P = 2 P A

, as required.

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