[" 4."P" is a point on the bisector of "/_ABC" .If the line through "P" ,parallel to "BA" meet "BC" at "Q" ,prove "],[" that "BPQ" is an isosceles triangle."],[" Solution."]

P is a point on the bisector of angle ABC .If the line through P , parallel to BA meet at Q ,prove that Delta BPQ is an isosceles triangle.

P is a point on the bisector of an angle /_ABC. If the line through P parallel to AB meets BC at Q, prove that triangle BPQ is isosceles.

P is a point on the bisector of angle ABC .If the line through P,parallel to BA meet at Q ,prove that BPO is an isosceles triangle.

P is a point on the bisector of an angle angleABC . If the line through P parallel to AB meets BC at Q. prove that triangle BPQ is isosceles.

P is a point on the bisector of an angle /_A B Cdot If the line through P parallel to A B meets B C at Q , prove that triangle B P Q is isosceles.

D and F are the mid-points of sides AB and AC of a triangle ABC. A line through F and parallel to AB meets BC at point E. Prove that BDFE is a parallelogram

In triangle ABC, P is the mid-point of side BC. A line through P and parallel to CA meets AB at point Q and a line through Q and a line through Q and parallel to BC meets median AP at point R. Prove that : BC=4QR .

In triangle ABC, the bisectors of angle B and angle C intersect at I. A line drawn through I and parallel to BC intersects AB at P and AC at Q. Prove that PQ = BP + CQ.

In triangle ABC, the bisectors of angle B and angle C intersect at I. A line drawn through I and parallel to BC intersects AB at P and AC at Q. Prove that PQ = BP + CQ.

In DeltaABC , the bisector of /_ABC intersects AC at the point P . Prove that CB: BA=CP:PA .