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In ΔABC, AB = AC, and the bisect are of angles B and C intersect at point O, then the ray AO
  • a)
    will bisect ∠A
  • b)
    will not bisect ∠A
  • c)
    AO = CO
  • d)
    AO = BO
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
In ΔABC, AB = AC, and the bisect are of angles B and C intersect...

∵ ∠B = ∠C

⇒ OB = OC ...(i)
(sides opposite to equal angles are equal)
Now,
In Δs ABO and ACO
AO = AO (common)
AB = AC (given)
OB = OC (From (i))
∴ ΔABO ≅ ΔACO
(By R-H-S congruence criterion)
∴ ∠BAO = ∠CAO = ∠A/2 (C.P.C.T)
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