Question

In the given figure, PT is tangent and PAB is a
secant to the circle. If the bisector of angle ATB
meets AB at M, then prove that angle ATM is

1/2( Angle PTA - Angle PAT)​

Answer 1

Answer:

As angle PTA = angle PTB ( tangent -angle theorem) (1)

And Angle BTM = angle MTA  (given) (2)

And angle PMT = angle PBT + angle MTB

So angle PMT = angle PTA + angle MTA (using (1) and (2) )

And angle PTA + angle MTA = PTM

So angle PMT = angle PTM ( hence proved)

In triangle PMT

We have angle PMT = angle PTM

So PM = PT (isosceles  triangle)

Step-by-step explanation: