Two parallel straight lines intersect three concurrent straight lines at the points `A`, `B`, `C` and `X,Y,Z` respectively. Prove that `AB : BC=XY : YZ`.

A straight line intersects one of the two concentric circles at the points A and B and other at the points C and D. Prove that AC = BD.

In trapezium ABCD , AB and DC are parallel. A straight line parallel to AB intersects AD and BC at the points E and F respectively. Prove that DE:EA=CF:FB .

AD is a median of triangleABC . A straight line parallel to BC intersect AB and AC at P and Q respectively. Prove that AD bisects PQ.

If the straight line intersects the circle at two points, then the straight line is called a "_____" to the circle.

In triangleABC , a straight line parallel to BC intersects AB and AC at P and Q respectively. If AB = 3PB, then PQ : BC =

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) .

If a straight line intersects the sides AB and AC of a triangle ABC at D and E respectively and is parallel to BC , then (AE)/(AC) = . ………..

The straight line PAB intersects the circle with centre O at the points A and B. The straight line PAB will be a tangent to that circle if AB ="_______"