Question

In ΔABC, P is the mid-point of BC. A line through P and parallel to CA meets AB at point Q, and a line through Q and parallel to BC meets median AP at point R. Prove that: AP = 2AR

Answer 1

In ΔABC,
P is the mid-point of BC and PQ is parallel to AC
Therefore, Q is the mid-point of AB.
In ΔABP,
Q is the mid-point of AB and QR is parallel to BP
Therefore, R is the mid-point of AP.
AR = RP
But AR + RP = AP
⇒ AR + AR = AP
⇒ 2AR = AP or AP = 2AR.