Question

Prove that “The centre lies on the bisector of the angle between the two tangents drawn from an
external point to a circle.”

Answer 1

Answer:

Given: PT and TQ are two tangent drawn from an external point T to the circle. To prove. \angle PTO = \angle QTO∠PTO=∠QTO where O is centre of circle. ... Centre lies on the bisector of the angle between the two tangents.

Answer 2

Answer:

Step-by-step explanation:

Given: PT and TQ are two tangent drawn from an external point T to the circle.

To prove :

∠PTO=∠QTO where O is centre of circle.

Construction: Join OT.

We know that a tangent to circle is perpendicular to the radius at the point of contact.

therefore,

∠OPT=∠OQT=90  

In triangle OPT and OQT,

OT = OT (Common)

OP = OQ ( Radii of the circle)

∠OPT=∠OQT (each is 90)

So, Triangle OPT and OQT (RHS congruence criterion)

PT = TQ and ∠OTP=∠OTQ (CPCT)

PT = TQ

Therfore

The lengths of the tangents drawn from an external point to a circle are equal.

∠OTP=∠OTQ

Therefore

Centre lies on the bisector of the angle between the two tangents.

So, option A is the answer.