ABC is an isosceles triangle, in which AB-AC , circumscribed about a c

1.	ABC is an isosceles triangle, in which AB-AC , circumscribed about a circle. Show that BC is bisected at thepoint of contact.
Answer» Ans :- Let the circle touches the side AB at P and side AC at Q and side BC at R We know that Tangents drawn from external points are equal. Then we have Tangents from point A i.e AP = AQ , Tangents from point B gives BP = BR , Tangents from point C gives RC = CQ. We have AB=AC ⇒ AP+PB=AQ +QC as AP= AQ ⇒ PB = QC ⇒ BR = RC This gives that BC is bisected at point of contact.

ABC is an isosceles triangle, in which AB-AC , circumscribed about a circle. Show that BC is bisected at thepoint of contact.

Answer»

Ans :- Let the circle touches the side AB at P and side AC at Q and side BC at R

We know that Tangents drawn from external points are equal.

Then we have Tangents from point A i.e AP = AQ , Tangents from point B

gives BP = BR , Tangents from point C

gives RC = CQ.

We have AB=AC ⇒ AP+PB=AQ +QC

as AP= AQ ⇒ PB = QC ⇒ BR = RC

This gives that BC is bisected at point of contact.