Question

In an Iscoceles triangle ABC, with AB=AC,The bisectors of ∠B and ∠C intersect each other at O..Join A to O ..Show that
(i)OB=OC
(ii)AO bisects ∠A.....

Answer 1

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Refer to he attachment..

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Answer 2

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Given,

AB = AC, the bisectors of ∠B and ∠C intersect each other at O

(i) Since ABC is an isosceles with AB = AC,

∴ ∠B = ∠C

⇒ 1/2∠B = 1/2∠C

⇒ ∠OBC = ∠OCB (Angle bisectors.)

⇒ OB = OC (Side opposite to the equal angles are equal.)

(ii) In ΔAOB and ΔAOC,

AB = AC (Given)

AO = AO (Common)

OB = OC (Proved above)

Therefore, ΔAOB ≅ ΔAOC by SSS congruence condition.

∠BAO = ∠CAO (by CPCT)

Thus, AO bisects ∠A.