Question

ABC is a right triangle right angled at A such that AB=AC and bisector of Angle C intersects the side AB at D.Prove that AC+AD=BC​

Answer 1

Answer:

ANSWER

Let AB=AC=a  and  AD=b.

△ABC is right angled at A ⇒  AB2+AC2=BC2  ⇒BC=a2

BD=AB−AD=a−b

By angle-bisector theorem, BDAD=BCAC.

⇒a−bb=a2a=21

⇒b=1+2a=a(2−1)

⇒a+b=a2

But, we know AC=a,   AD=b,   BC=a2

⇒AC+AD=BC.   Hence it is proved.