Question

ABC is a right triangle with AB = BC. Bisector of ∠B meets AC at D. Prove that

AC = 2BD.​

Answer 1

AC = 2 BD if ABC is a right triangle with AB = BC. Bisector of ∠B meets AC at D

Step-by-step explanation:

ABC is a right triangle with AB = BC.

∠B = 90°

=> ∠A = ∠C = 45°  (as AB = BC)

Bisector of ∠B = 90°/2 = 45°

in ΔABD

∠A = ∠ABD = 45°

=> AD = BD

Similarly

in ΔCBD

∠C = ∠CBD = 45°

=> CD = BD

AC = AD + CD

=> AC = BD + BD

=> AC = 2 BD

QED

Proved

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