A line L intersects three sides BC, CA and AB of a triangle in P,Q,R respectively, show that `(BP)/(PC).(CQ)/(QA).(AR)/(RB)=-1`

if a line intersects sides AB and AC of a DeltaABC at D and E respectively and is parallel to BC, prove that (AD)/(AB)=(AE)/(AC) (see Fig. 6,13).

Through A,B and C lines RQ,PR and QP have been drawn, respectively parallel to sides BC, CA and AB of a triangleABC as shown in fig. show that BC=1/2QR

If D, E and F are three points on the sides BC, CA and AB, respectively, of a triangle ABC such that the lines AD, BE and CF are concurrent, then show that " "(BD)/(CD)*(CE)/(AE)*(AF)/(BF)=1

Let A, B, C respresent the vertices of a triangle, where A is the origin and B and C have position b and c respectively. Points M, N and P are taken on sides AB, BC and CA respectively, such that (AM)/(AB)=(BN)/(BC)=(CP)/(CA)=alpha Q. AN+BP+CM is

Let A, B, C represent the vertices of a triangle, where A is the origin and B and C have position b and c respectively.* Points M, N and P are taken on sides AB, BC and CA respectively, such that (AM)/(AB)=(BN)/(BC)=(CP)/(CA)=alpha . If triangle represent the area enclosed by the three vectors AN, BP and CM, then the value of alpha , for which triangle is least

XY is a line parallel to side BC of triangle ABC. If BE II AC and CF II AB meet XY at E and F respectively,show that ar (ABE) = ar (ACF).

P and Q are respectively the midpoints of sides AB and BC or a triangle ABC and R is the mid-point of AP, show ar(PRQ)= 1/2 ar(ARC).

P and Q are respectively the midpoints of sides AB and BC or a triangle ABC and R is the mid-point of AP, show ar(PBQ)=ar(ARC).

If P,Q and R are the mid-point of the side BC,CA and AB of a triangle and AD is the perpendicular form A and BC, prove that P,Q and D are concylic.

A line parallel to BC of a triangle ABC, intersects AB and AC at D and E respectively. Prove that (AD//DB) =( AE//EC) .