Question

Tangents drawn from an external point to a circle subtend ________ angles to the centre.

Answer 1

PA and PB are two tangents drawn from P to circle with centre O. OP is the line segment joining the point P and centre of the circle.

In ∆OAP and ∆OBP,

OA = OB (Radius of the circle)

OP = OP (Common)

∠OAP = ∠OBP (Radius is perpendicular to the tangent at the point of contact)

∴ ∆OAP $\cong$ ∆OBP (RHS congruence criterion)

⇒ ∠AOP = ∠BOP (CPCT)

Hence, the tangents drawn from an external point to a circle subtend equal angles to the centre.
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Tangents drawn from an external point to a circle subtend __equal__ angles to the centre.