Question

if abc is a equilareral triangle inscribed in a circle and p is a pt on minor arc bc which do not coincide with b or c then prove that pa is angle bisector of angle bpc

Answer 1

AB=BC=AC
so chord AB=chord AC
∠Aob=∠Aoc
wkt angle subtended by an arc at the centre is twice the angle subtended by same arc,
Now consider the arc AB,
∠AOB=2∠APB
consider arc AC,
∠AOC=2∠APC
     now we get 2∠APB=2∠APC
                         ∠APB=∠APC

AP is the bisector of ∠BPC