Two tangents PA and PB are drawn from an external point P to the circle with centre O, such that ∠ APB = 120 ∘ what is the relation between OP and AP? Options: A . &nbspOP = 12 AP B . &nbspAP = 23 OP C . &nbspOP = 2 AP D . &nbspOP = AP

Two tangents PA and PB are drawn from an external point P to the circle with ce

Question

Two tangents PA and PB are drawn from an external point P to the circle with centre O, such that

∠

APB =

120^{\circ}

what is the relation between OP and AP?

Options:

A . OP = 12 AP

B . AP = 23 OP

C . OP = 2 AP

D . OP = AP

Answer: Option C
:
C

Two Tangents PA And PB Are Drawn From An External Point P t...

Given that

∠ A P B = 120^{\circ}

Also, we know that if two tangents are drawn from an external point to a circle, then the line joining the external point and the centre of the circle bisects the angle between the tangents.

⟹ ∠ A P O = ∠ O P B = 60^{\circ}

Thus, cos

∠ O P A = c o s 60^{\circ} = \frac{A P}{O P}

⟹ \frac{1}{2}

\frac{A P}{O P}

Thus,

O P = 2 A P

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