# Q.1. ** #AD bisects the angle A of a triangle ABC and meets BC at D such that BD/DC=AB/AC . If BC=k,CA=l,and AB=m (all are in meters), then find the length of DC(in metres)**

# Solution : since AD bisects angle A of triangle ABC

therefore;

## AD is angle bisector of angle BAC ,

## therefore;

## BD/DC=AB/AC ………………….. (angle bisector theorem);

## DC/BD=AC/AB ………………….. (Invertendo);

## Therefore

## (BD+DC)/BD=(AB+AC)/AB …………..(Componendo);

## BC/BD=(AB+AC)/AB ………………….(B-D-C) ;

## BC*AB=BD(AB+AC) ………………….. (Cross multiplication);

## (BC*AB)/(AB+AC)=BD……………… (transposing ( AB+AC )to the R.H.S);

## k*m/(m+l)=BD ;

## i.e BD=k*m/(m+l) meters ………… (Since , BC=k;AB=m;CA=l) ,