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: BC = 4QR

Answer 1

In ΔABC,
Q and S are the mid-points of AB and AC respectively. Also QS is parallel to BC

Therefore, QS = `(1)/(2)"BC"`       ......(i)

Now, AP is the median, hence it bisects BC and QS
Therefore

`(1)/(2)"QS"` = QR

⇒ QS = 2QR

Substituting in (i)

⇒ 2QR = `(1)/(2)"BC"`

⇒ BC = 4QR.