`P, Q, R` are the points of intersection of a line t with sides `BC, CA, AB` of a `DeltaABC` respectively, then `(BP)/(PC).(CO)/(QA).(AR)/(RB)=`

P,Q,R are the points of intersection of a line t with sides BC,CA,AB of a Delta ABC respectively,then (BP)/(PC)*(CO)/(QA)*(AR)/(RB)=

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

A(x_1,y_1), B(x_2,y_2),C(x_3,y_3) are three vertices of a triangle ABC, lx+my+n=0 is an equation of line L. If L intersects the sides BC,CA and AB of a triangle ABC at P,Q,R respectively, then (BP)/(PC)xx(CQ)/(QA)xx(AR)/(RB) is equal to

If the vectors bara, barb and barc from the sides BC, CA and AB, respectively, of DeltaABC , then

D, E and F are respectively the mid-points of the sides BC, CA and AB of a DeltaABC . Show that ar(BDEF) = 1/2ar(triangleABC)

A line cuts two sides AB and AC of DeltaABC at points P and Q respectively. Prove (A(DeltaAPQ))/(A(DeltaABC))=(APxxAQ)/(ABxxAC) .

If DeltaABC is a equilateral triangle and P, Q, R are mid-points of sides AB, BC and CA respectively then-