CBSE Class 10 Maths (Standard) 2015 · Paper 30/1 · Question 5

Circles 2 marks Medium

In Figure 3, two tangents

R Q

and

R P

are drawn from an external point

R

to the circle with centre

O

. If

∠ P R Q = 12 0^{\circ}

, then prove that

O R = P R + R Q

Figure 3

Answer

Since

∠ O R P = 6 0^{\circ}

and

∠ O P R = 9 0^{\circ}

cos 6 0^{\circ} = P R / O R

gives

O R = 2 P R

; with

P R = R Q

O R = P R + R Q

. Proved.

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