in circle, TP is a tangent and PAB is a secant to the circle. If the bisector of angleATB intersects AB at M, show that
1 angle PMT= anglePTM
2 PT=PM
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)