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Is the following statement true or false?

$R Q$ and $R P$ are two tangents drawn from an external point $R$ to the circle with centre $O$ . If $∠ P R Q = 120 °$ , then $O R = P R + R Q$ .

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True

False

answer is A.

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Detailed Solution

Given,

R Q and R P

are two tangents which are drawn from an external point.

∠ P R Q = 120 °

O P = O Q

[Radius of the circle]
We have

∠ P R Q = 120 °

,
We also know that the tangents drawn from an external point are of the same length.

∠ O R P = 120 ° 2 ∠ O R P = 60 °

P R = R Q

…..i)
Applying the cosine of the angle in

Δ O R P

using equation i),

cos 60 ° = P R O R 12 = P R O R O R = 2 P R O R = R P + R Q

Thus,

O R = P R + R Q

which is true.
Therefore the correct option is 1.

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