Tangent to the circle with Centre O V biceps AP prove that triangle AEO is similar to triangle ABC

Tangent to the circle with Centre O V biceps AP prove that triangle AE

1.	Tangent to the circle with Centre O V biceps AP prove that triangle AEO is similar to triangle ABC
Answer» According to question we are given that BC is tangent with centre O and OE bisects APIn {tex}\\Delta{/tex}AOP,OA = OP (radii) {tex}\\Delta{/tex}AOP is an isosceles triangle. OE is a median.Since a perpendicular to a circle from a center to a chord bisects it.{tex}\\therefore \\angle OEA = 90^\\circ {/tex}In {tex}\\Delta{/tex}AOE and {tex}\\Delta{/tex}ABC,{tex}\\angle ABC = \\angle OEA = 90^\\circ{/tex}{tex}\\angle A{/tex} is common.{tex}\\Delta{/tex}AEO ~ {tex}\\Delta{/tex}ABC ..…(AA test)