Two circles with centres O and O'are drawn to intersect each other at points A and B. Centre O of one circle lies on the circumference of the other circle and CD is drawn tangent to the circle with centre O' at A. prove that OA bisects angle BAC.

The congruent circles with centres Oand O' intersect at two points A and B. Then, angleAOB=angleAO'B .

In Figure, B C is a tangent to the circle with centre OdotO E bisects A Pdot Prove that A E O ~ A B Cdot

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.

Construct a circle with centre O and radius 4 cm.

Two equal chord AB and CD of a circle with centre O, intersect each other at point P inside the circle. Prove that: BP = DP

. In the given figure, two equal circles, with centres O and O', touch each other at X. OO' produced me the circle with centre O' at A. AC is tangent to the circle with centreO, at the point C. O'D is perpendicular to AC. Find the value of (DO')/(CO) .

. In the given figure, two equal circles, with centres O and O', touch each other at X. OO' produced me the circle with centre O' at A. AC is tangent to the circle with centreO, at the point C. O'D is perpendicular to AC. Find the value of (DO')/(CO) .

In Figure 2, AB and AC are tangents to the circle with centre O such that angle BAC = 40°. Then angle BOC is equal to

Two circles with equal radii are intersecting at the points (0, 1) and (0,-1). The tangent at the point (0,1) to one of the circles passes through the centre of the other circle. Then the distance between the centres of these circles is.

In Figure, two tangents A Ba n dA C are drawn to a circle with centre O such that /_B A C=120^0dot Prove that O A=2A B