question_answer

D is any point on side AC of a \[\Delta ABC\] with AB = AC. Then ____.

A)  CD < BD        

B)         CD>BD          

C)         CD = BD      

D)         None of these

Correct Answer: A

Solution :

In \[\Delta \Alpha \Beta C,D\]is any point on side Ac and AB = AC. Now in \[\Delta ABC,AC=AB\] \[\therefore \]\[\angle ABC=\angle ACB\]                           ?(1) [Angles opposite to equal sides of a\[\Delta \]are equal] And \[\angle ABC=\angle ABD+\angle DBC\] \[\Rightarrow \]\[\angle ABC>\angle DBC\] \[\Rightarrow \]\[\angle ACB>\angle DBC\]             [From (1)] \[\Rightarrow \]\[BD>CD\][Side opposite to greater angle is longer] or \[CD>BD\]