A straight line L interesect the sides BC, CA and BA of `triangleABC` at P,Q and R resp. Prove that `(PR)/(PQ).(CQ)/(AC).(AB)/(RB) = 1`.

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

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

The diagonals AC and BD of the parallelogram ABCD intersect each other at O . Any straight line passing through O intesects the sides AB and CD at the points P and Q respectively . Prove that OP = OQ.

The two points P and Q are on a straight line, At the points P and Q , PR and QS are perpendicular on the straight line. PS and QR intersect each other at the point O . OT is perpendicular on PQ . Prove that (1)/(OT)=(1)/(PR)+(1)/(QS) .

In DeltaABC a straight line parallel to BC intersects the sides AB and AC at the points P and Q respectively. If AP=QC , AB=12cm , AQ=2cm , then find the value of CQ .

The straight line parallel to the side BC of DeltaABC intersects the sides AB and AC at the points D and E respectively. Then (AB)/(BD)=(AC)/(CE) .

Two circles intersect each other at the points P and Q. Two straight lines through P and Q intersect on circle at the points A and C and the other circle at B and D . Prove that AC||BD.

The diameters of the circumcirle of triangle ABC drawn from A,B and C meet BC, CA and AB, respectively, in L,M and N. Prove that (1)/(AL) + (1)/(BM) + (1)/(CN) = (2)/(R)

In triangleABC , a straight line parallel to BC intersects the sides AB and AC at P and Q respectively. If AP = 8cm, CQ = 9cm and AQ = 2BP, then BP=

If a, b, c are in H.P., prove that, (1)/(bc), (1)/(ca), (1)/(ab) are in H.P.