Question

in an isosceles TRIANGLE ABC, WITH AB=AC, THE BISECTOR OF ANGLE B AND ANGLE C INTERSECT EACH OTHER AT O. JOIN A TO O

Answer 1

b=c
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Answer 2

Answer: To Find: (i) OB = OC   (ii) AO bisects <A

(i) Consider, ΔAOB ≅ ΔAOC

= AB = AC (Given)

= <B = <C (∵ AB = AC)

= 1/2 <B = 1/2 <C

= <ABO = <ACO (Opposite angles)

= OA = OA (Common Side)

∴ By SAS Congruence rule,

= ΔAOB ≅ ΔAOC (C.P.C.T)

= <BAD = <OAC (CPCT)

= OB = OC (CPCT)

(ii) Show that AO bisects <A

= AO bisects <A (CPCT)

= ΔAOB ≅ ΔAOC