ABCD is a parallelogram, P is the mid-point of AB . If R is the point of intersection of AC and DP , then R divides AC internally in the ratio

Step-by-step solution

Draw BS parallel to DP as shown Let A P=P B=x D S=x S C=x B A Q P A R AB AP = AQ AR 2 x x = AQ AR AQ =2 AR Thus R is mid point of AQ . i.e. AR = RQ Similarly CQS CRD CQ = RQ Thus we get AR = RQ = CQ Hence point R divides A C in the ratio 1: 2