Question

The two tangents drawn from an external point to a circle are _______ to the segment joining the centre to the point.

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)

⇒ ∠APO = ∠BPO (CPCT)

Hence, the two tangents drawn from an external point to a circle are equally inclined to the segment joining the centre to the point.


The two tangents drawn from an external point to a circle are _equally inclined_ to the segment joining the centre to the point.