The two circles with centre X and Y intersect each other at the points A and B, A joined with the mid -point S of XY and the perpendicular on SA through the point A is drawn which intersect the two circles at the point P and Q .Prove that PA = AQ.

Two circles with centres A and B intersect each other at points P and Q. Prove that the centre-line AB bisects the common chord PQ perpendicularly.

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 .

Three points P,Q ,R lie on a circle. The two perpendiculars PQ and PR and the point P intersect the circle at the points S and T respectively. Prove that RQ=ST

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 .

The centre of two circle are P and Q they intersect at the points A and B. The straight line parallel to the line segment PQ through the point A intersects the two circles at the point C and D Prove that CD = 2PQ

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 .

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.

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.

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 circles intersect each other at point P and Q. Secants drawn through p and Q intersect the circles at points A,B and D,C Prove that : /_ ADC + /_ BCD = 180^(@)