Question

prove that any point of the bisector of an angle is equidistant from the arm of the angle​

Answer 1

we need to show BP=CP

in right angles △ABP

sinα=APBP...(i)

in right angled △ACP 

sinα=APCP...(ii)

from (i) & (ii)

APBP=APCP

BP=CP

Hence Proved.