ABC is a triangle inside the circle .D and E are points on AB and AC respectively. AB and AC are two chords of circle whose centre is o. If OD is perpendicular

Question

ABC is a triangle inside the circle .D and E are points on AB and AC respectively. AB and AC are two chords of circle whose centre is o. If OD is perpendicular to AB , OE is perpendicular to AC and AO bisects angle DAE , Prove that triangle ADE is an isosceles triangle and angle ABC = angle ACB.

Answer 1

Draw and label a diagram.

∠AOD ≅ ∠AOE

ΔAOD ≅ ΔAOE  ASA

AD ≅ AE                  corresponding parts

ΔADE is isosceles     by definition