Two circles whose centres are `O` and `O '` intersect at `Pdot` Through `P ,` a line `l` parallel to `O O '` intersecting the circles at `C\ a n d\ D` is drawn. Prove that `C D=2\ O O '`

Two circles whose centres are O and O' intersect at P. Through P, a line l parallel to OO' intersecting the circles at C and D is drawn.Prove that CD=2OO

Two circles with centres O and O' intersect at P. Through P, a line 'l' parallel to a OO', meeting circles at C and D, is drawn. Prove that CD = 2OO'

Two cocentric circle common centre O. A line 'l' intersects these circle A,B,C and D. Prove that AB = CD.

The diagonals of a parallelogram A B C D intersect at O. A line through O intersects A B\ at X\ a n d\ D C at Y . Prove that O X=O Y .

In the given figure, two circles with centres O and O' touch externally at a point A. A line through A is drawn to intersect these circles at B and C. Prove that the tangents at B and C are parallel.

The diagonals of a parallelogram A B C D intersect at OdotA line through O intersects A B\ at X\ a n d\ D C at Ydot Prove that O X=O Y

In Figure, O is the centre of a circle and P O BISECTS /_A P D . Prove that A B=C D

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.

Two circle with centre O and P intersect each other in point C and D. Chord AB of the circle with centre O touches the circle with circle with centre P in Point E. Prove that angleADE+angleBCE= 180^(@)

The diagonals of a parallelogram A B C D intersect at OdotA line through O intersects A B at X and D C at Ydot Prove that O X=O Ydot