Question

In the given figure, ∠CAB = ∠CBA, D and E are points on the sides BC and AC respectively of ∆ABC such

that BD = AE. If O is the point of intersection of AD and BE, then prove that OA = OB.​

Answer 1

Hope this will help you mate

Answer 2

Given : ∠CAB = ∠CBA

D and E are points on the sides BC and AC respectively of ∆ABC such

that BD = AE.

O is the point of intersection of AD and BE,

To Find : prove that OA = OB.​

Solution:

∠CAB = ∠CBA

=> ∠EAB = ∠DBA     as D and E are points on the sides BC and AC respectively

in ΔABE & ΔBAD

AE = BD   Given

∠EAB = ∠DBA  

AB = AB     Common

=>  ΔABE ≅ ΔBAD  ( ASA)

=>  ∠AEB = ∠BDA

∠AEO = ∠BDO

in ΔAEO and ΔBDO

AE = BD

∠AEO = ∠BDO

∠EOA = ∠DOB  ( vertically opposite angle )

=> ΔAEO ≅ ΔBDO

Hence OA = OB

QED

Hence Proved

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