E is the mid-point of a median AD of DABC and BE is produced to meet AC at F. Show that AF = AC.

Question

Philoid · Accepted Answer

Given, a ABC in which AD is a median and E is mid-point of AD. Now, drawing DP||EF.

In ΔADP, E is mid-point of AD and EF||DP.

F is mid-point of AP.

In ΔFBC, D is mid-point of BC and DP||BF.

P is mid-point of FC.

Thus, AF = FP = PC

Hence, AF = AC

Hence, proved.