Question

If the angle between two tangents drawn from an external point 'P' to a circle of radius ' and
centre 'O' is 30°, then find the length of OP​

Answer 1

✯ᗅℕՏᗯℰℛ✯

Let PQ and PR be two tangents drawn from P to the circle with center 'O'.Given,

                ∠RPQ = 60°

OP is angle bisector of ∠RPQ

                ⇒ ∠OPQ = ∠OPR = 30°

Let 'a' be the radius of the circle.

                ⇒ OQ = OR = a

Now, PQ⊥OQ and PR⊥OR    [∵ tangent is perpendicular to radius]From ΔOPQ,

                    sin30=\frac{OQ}{OP}sin30=OPOQ

                     \frac{1}{2}=\frac{a}{OP}21=OPa

                ⇒ OP = 2a units

$thanks$

                   

Answer 2

Step-by-step explanation:

OA=a

OP=?

ANGLE BETWEEN TANGENTS=60°

Tangents are equally aligned to each other

=> <OPA=<OPB=30°

IN ∆OPA,

<POA=180°-90°-30°

=60°

Cos 60°=OA/OP

1/2 =a/OP

=> OP = 2a(Ans)