in an isoscele triangle ABC with ab=ac the biscectors of ABC and BCA intersect each other at O. join A to O. show that OB=OC
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Step-by-step explanation:
Solution:-
Solution:-Given:-
AB = AC and
the bisectors of B and C intersect each other at O
(i) Since ABC is an isosceles with AB = AC,
B = C
½ B = ½ C
⇒ OBC = OCB (Angle bisectors)
∴ OB = OC (Side opposite to the equal angles are equal.)
(ii) In ΔAOB and ΔAOC,
AB = AC (Given in the question)
AO = AO (Common arm)
OB = OC (As Proved Already)
So, ΔAOB ΔAOC by SSS congruence condition.
BAO = CAO (by CPCT)
Thus, AO bisects A.
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