IIMB 2001 (QA) PYQs

In triangle $ABC$, let $D$ be a point on side $BC$ such that $AD$ is the angle bisector of $\angle BAC.$ If $AB=8$ cm, $AC=6$ cm, and $BC=10$ cm, what is the length of $BD$?

$D$ is a point on side $A C$ of a triangle $A B C$ such that $A D=B D, C D=B C$ and $\angle B A C=30^{\circ}$. Then, $\angle A B C+\angle B D C$ is equal to:

In triangle $AD \perp BC, BE \perp AC$ and $CF \perp AB$. $AD, BE$ and $CF$ intersect each other at $O$. If $AO=18$ cm, $BO=12$ cm and $AD=20$ cm then what is the length of $BE$?