Question

in the figure bd=ab and bd²=be×bc . prove that ad bisects angle cae?​

Answer 1

Answer:

Given :

• BD bisect ZABC.

To Prove :

• AB / BD = BE / BC.

Construction :

• Join DC.

Solution :

In AABE and ADBC, we have,

ZABEZDBC. [BD is angle bisector of <ABC .}

→ ZBAE = 2BDC. (All angles inscribed

➜ ZBAE = <BDC. { All angles inscribed

in a circle and subtended by the same chord are equal. }

So,

→ AABE = ADBC . { By AA Similarity. }

Therefore,

→ AB/BE = DB/BC.

Or,

→ AB / DB = BE / BC . { cross - Multiply. }

Hence,

→ AB/BD = BE/BC. (Proved.)