Two circles of equal radii intersect each other at the point A and B. A straight line passing throught A intersects the two circles at the points P and Q , where Q are on the opposite sides of AB. Prove that PB=PQ

Like the adjoining figure, draw two circles with centres C and D which intersect each other at the points A and B . Draw a straight line through A which intersects the circle C at the point P and the circle with centre D at the point Q. Prove that (i) angle PBQ= angle CAD (ii) angle BPC= angle BQD .

In two circles , one circle passes through the centre O of the other circle and they intersect each other at the points A and B . A straight line passing through A intersect the circle passing through O at the point P and the circle with centre at O at the point R . BY joining P , B and R , B prove that PR= PB.

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.

Two circles intersect each other at the points G and H . A straight line is drawn through the point G which intersect two circles at the points P and Q and the straight line through the point H parallel to PQ intersects the two circles at the points R and S . Prove that PQ=RS .

Two circles intersect each other at the points P and Q. A straight line passing through P intersects one circle at A the other circle at .A straight line passing through Q intersect the first circle at C and the second circle at D. Prove that AC||BD .

Two circle intersect each other at A and B and a straight line parallel to AB intersects the circles at C,D,E,F. Prove that CD = EF.

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 .

Each of the two equal circles passes through the centre of the other and the two circles intersect each other at the points. A and B.If a straight ine through the point A intersects the two circles at points C and D prove that Delta BCD is an equilateral triangle.

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.

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.