Two circles intersect at two points A and B AD and AC are diameters to the two circles Prove that B lies on the line segment DC.

Two circles intersect at two points B and c. Through B, two line segments ABD and PBQ are drawn to intersect the circles at A, D and P, Q respectively (see the given figure). Prove that angle ACP = angle QCD.

Two magnetic lines intersect ? Why ?

If A and B are any two sets, prove that P(A) = P(B) implies A = B.

A line intersecting a circle in two points is called a secant.

If two circles intersect at two points, prove that their centres lie on the perpendicular bisector of the common chord.

If two circles intersect at two points, then prove that their centres lie on the perpendicular bisector of the common chord.

Two different non-parallel lines meet the circle abs(z)=r . One of them at points a and b and the other which is tangent to the circle at c. Show that the point of intersection of two lines is (2c^(-1)-a^(-1)-b^(-1))/(c^(-2)-a^(-1)b^(-1)) .

Two circles of radii 5 cm and 3 cm intersect at two points and the distance between their centres is 4 cm. Find the ength of the common chord.

If circles are drawn taking two sides of a triangle as diameters, prove that the point of intersection of these circles lie on the third side.