 Good morning friends. I am Purva and today we will discuss the following question. In figure one we have DE is parallel to AB and FE is parallel to DB and we have to prove that DC square is equal to CF into AC. Let us begin with the solution now. Now we are given triangle ABC in which DE is parallel to AB and FE is parallel to DB and we have to prove that DC square is equal to CF into AC. Now first we consider triangle CAB. So in triangle CAB we have DE is parallel to AB. This is given to us. Therefore by basic proportionality theorem which states that if a line is drawn parallel to one side of a triangle the other two sides are divided in the same ratio. We have DC upon AC is equal to CE upon BC. We mark this as equation 1. Similarly in triangle CDB we are given that FE is parallel to DB. Therefore again by basic proportionality theorem we have CF upon DC is equal to CE upon BC. We mark this as equation 2. So from 1 and 2 we get right hand side of both the equations 1 and 2 are same. So we get DC upon AC is equal to CF upon DC. Or we can write this as DC into DC is equal to CF into AC. Or DC square is equal to CF into AC. Thus we have proved that DC square is equal to CF into AC. This is our answer. Hope you have understood the solution. Bye and take care.