ABC is a triangle in which angle B=2*angle C. D is a point on BC such that ad bisects angle BAC &AB=CD prove that angle BAC=72 degree.
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refer to diagram
A + B + C = 180 => A = 180 - 3C
t = A/2 = 90 - 3/2 C
a / sin A = b / sin B = c / sin C
A + B + C = 180 => A = 180 - 3C
t = A/2 = 90 - 3/2 C
a / sin A = b / sin B = c / sin C
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kvnmurty:
net connection was cut off while answering this question. I will complete.
AB/sin (C+t) = AD/sin 2C ; CD/sin t = AD/sin C ; AB = CD => sin (C+t) = 2 cos C sin t = sin (c+t) + sin (C-t) => sin C-t =0 => C = t => 5/2 C = 90 deg => C = t = 36. => B = 72 deg
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