Question

Prove that centre of circle lies on bisector of angle between tangents​

Answer 1

Given:

PT and TQ are two tangents drawn from an external point T to the circle (O, r).

To prove :

♦PT=TQ

♦angle QTP = angle OTQ

Construction:

Join OT

Proof:

We know that, Tangent to circle is perpendicular to the radius through the point of contact.

therefore, angle OPT = angle OQT = 90°

In ∆OPT and ∆OQT ,

OT = OT (common)

OP = OQ (radius of the circle)

angle OPT= angle OQT(RHS congruence rule)

PT = TQ and angle OTP = angle OTQ(CPCT)

PT = TQ

therefore, The lengths of the tangent drawn from an external point to a circle are equal.

angle OTP = angle OTQ

therefore, centre lies on the Bisector of the angle between the two tangents.

$<marquee>❤ItzSmartGirl❤</marquee>$

Answer 2

Step-by-step explanation:

this is the process aese hi dekh k kr lo bhai aa jaega aagr dono ka nikalna ho