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 .

Ankita drew two circles which intersect each other at the points P and Q. Through the point P two straight lines are draw so that they intersect one of the circle at the points. A and B and the ohte circle at the points C and D respectively. Prove that angle AQC= angle BQD .

If 5 parallel straight lines are intersected by 4 parallel straight lines then the number of parallelograms thus formed is

Two straight lines are drawn through any point X and exterior to a circle to intersect the circle at points A, B and points C, D respectively . Prove that DeltaXACandDeltaXBD are equiangular.

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.

Two two circle with their centre at P and Q intersect each other, at the point A and B . Through the point A , a straight line parallel to PQ intersects the two circles at the points C and D respectively . If PQ = 5 cm , then determine the lenght of CD .

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) .