Question

In triangle abc it is given that ab=ac and the bisects of angle b and angle c intersected at o . If b is point on ao produce . Prove that angle moc=angle abc and draw figure

Answer 1

ABC is a right angled triangle with <A = 90 deg and AB = AC = m (say), To prove that AC+AD = BC. Proof: In triangle ABC, BC = m√2 being the hypotenuse.

<B = <C = 45 deg, so <ACD = <BCD = 45/2 = 22.5 deg. AD = m tan 22.5 = 0.414213562 m= (√2–1)m. AC +AD = m + (√2–1)m = √2m = BC. Proved.