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

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)=

If D,E and F are three points on the sides BC,CA and AB, respectively,of a triangle ABC such that the (BD)/(CD),(CE)/(AE),(AF)/(BF)=-1

A line L cuts the sides AB,BC of ABC in the ratio 2:5,7:4 respectively then the line L cuts CA in the ratio

A circle is inscribed in a triangle ABC. It touches sides AB, BC and AC at the points P, Q and R respectively. If BP=8.5cm, CQ= 6.5cm and AR=4.5cm,then the perimeter (in cm) of the triangle ABC is: त्रिभुज ABC के अंदर एक वृत्त बनाया गया है| यह AB, BC और AC भजाओुं को क्रमशः P, Q और R बिंदुओं पर स्पशे करता है| अगर BP=8.5cm, CQ= 6.5cm और AR=4.5cm है, तो triangle ABC की परिमिति (cm में) हैः

Through A, B and C lines RQ, PR and QP have been drawn, respectively parallel to sides BC, CA and AB of a Delta ABC as shown in figure. Show that BC=(1)/(2)QR .

25.In figure,the sides AB,BC and CA of triangle ABC touch a circle with centre and radius r at P,Q and R respectively.Prove that (i) AB+CQ=AC+BQ (ii) Area Delta ABC=(1)/(2) perimeter of Delta ABC).r