Question

AB = AC . D is a point of ac such that BC^2 = ACxCD . Prove BD = BC

Answer 1

Given △ABC in which AB = AC and D is a point on the side AC 


such that BC^2 = AC x CD 

To prove: BD = BC 

Construction: Join B to D 

Proof: 

We have BC^2 = AC x CD 

=> BC/CD = AC/BC 

Thus in △ABC and △BDC, we have 

AC / BC = BC / CD .................(i) 

and ∠C = ∠C [Common] 

Therefore, △ABC = △BDC 

=> AB / BD = BC / CD .........(ii) 

From (i) and (ii), we get 

AC / BC = AB / BD 

∴BD = BC (∵AB = BC)


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