Question

in a triangle ABC P is the midpoint of side BC a line through p and parallel to ca meet at point to point Q and a line through q and parallel to BC meets median AP at. R prove that a b is equals to 2 BC is equals to 4 QR

Answer 1

Answer:

BC = 4QR

Step-by-step explanation:

P is mid point of Side BC

& PQ ║ CA

=> ΔBPQ ≈ ΔBCA

=> BP/BC = BQ/AB = PQ/AC

BP = BC/2  ( as P is mid point)

=> BP/BC = 1/2

=> BQ/AB = PQ/AC = 1/2

=> AB = 2BQ    & AC = 2PQ

AB = 2BQ = AQ + BQ  => BQ = AQ

=> AB = 2AQ

=> AQ/AB = 1/2

QR ║ BC

=> QR ║ BP  as P lies on BC

=>  ΔAQR ≈ ΔABP

=> AQ/AB  = AR/AP = QR/BP

using  AQ/AB = 1/2

=> AR/AP = QR/BP = 1/2

=> BP = 2QR

P is mid point of BC

=> BC = 2BP

=> BC = 2 * 2QR

=> BC = 4QR