Question

5. In the given figure, PM is a tangent to the circle and PA = AM.
Prove that ∆ PMB is isosceles.​

Answer 1

Proved that ∆ PMB is isosceles.

To prove : ΔPMB is isosceles.

Given : PM is a tangent to the circle and PA = AM.

From the figure,

In ΔPAM,

∠APM = ∠AMP   -----> ( 1 )

PA = AM

By using, alternate segment property of tangent.

∠ABM = ∠AMP   -----> ( 2 )

From equation ( 1 ) and ( 2 ), we get

∠APM = ∠ABM

PM = MB    

SO, ΔPMB is an isosceles.

Hence proved.

To learn more...

1. In the given fig. PA and PB are tangents to the circle with centre O. Prove that OP bisects AB and is perpendicular to it.

brainly.in/question/3141757

2. TA is the tangent to a circle from a point T and TBC is a secant to a circle if th AB is the bisector of angle ACB then show that triangle ADT is an isosceles triangle.

brainly.in/question/2850243