Question

abc is an isosceles triangle inscribed in a circle and AB=AC the bisector of angle B and angle C meet the the circumference at X and Y respectively prove that BY= AX​

Answer 1

Given :  abc is an isosceles triangle inscribed in a circle and AB=AC the bisector of angle B and angle C meet the the circumference at X and Y respectively

To find :  BY = AX

BX = CY

Solution:

ΔABC  is isosceles triangle

AB = AC

=> ∠B = ∠C

BX bisector of angle B

=> ∠ABX =   ∠B/2

CY is bisector of angle C

=> ∠BCY = ∠C/2

∠B = ∠C

=> ∠ABX  = ∠BCY  

=> AX = BY

chord subtending equal angles are congruent .

QED

Hence Proved

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Answer 2

Step-by-step explanation:

To find: BY=AX

BX=CY

SOLUTION: ABC is isosceles triangle

AB= AC

= <b=<c

BX bisector of angle B

<ABX =<B/2

CY is bisector of angle C

<BCY =<C/2

<B=<C

<ABX=<BCY

AX=BY (Chord subtending equal angles are congruent)

QED