Question

Triangle ABC is isosceles in which AB=AC circumscribed about a circle. Prove that base is bisected by the point of contact.

Answer 1

let base be bisected at x ,then,ap=aq(tangents).
AB=AC,AP=AQ THEREFORE,AB-AP=AC-AQ.
That is PB=CQ----1
But BP=BX and QC=CX (tangets) -----2
Fom 1 and 2,we prove BX=CX

Answer 2

Answer:

Given that,

AB=AC

Step-by-step explanation:

there are 3 pairs of tangents

AR=AQ-------------1

BR=BP--------------2

CQ=CP-------------3

AB=AC   [Given]

AR+BQ=AQ+CQ

AR+BQ=AR+CQ    [From 1]

BQ=CQ

BP=CP    [From 2 & 3]

Hence, proved that point of contact of the base(P) bisects BC.