Question

AB&AC are 2 chords of a circle whose centre is O if OD is perpendicular to AB ,OE perpendicular to AC.& AO bisects angle DAE. prove that triangle ADE is a isoseles triangle. and angle ABC =angle ACB

Answer 1

Draw and label a diagram.∠AOD ≅ ∠AOEΔAOD ≅ ΔAOE  ASAAD ≅ AE corresponding partsΔADE is isosceles by definition

Answer 2

In triangle OAE and OAD, OA = OA∠DAO= ∠EAO [Given ]∠OEA=∠ODA= 90 degreeSo, △OAE≅△OADSO AE = AD And hence triangle AED is an isosceles triangle. Now, We know that perpendicular from the centre divides the side in two equal partso 2AE=2ADAC = AB SO angle ABC = angle ACB