In the figure given below, two circles intersect at A and B, and AC, AD are respectively the diameters of the circles. Prove that the points C,B,D are collinear.

Explanation

GIVEN Two circles C(O,r) and C(O',r') with AC and AD as diameters respectively, intersecting at A and B.
TO PROOVE Point C,B,D are collinear.
CONSTRUCTION Join CB, BD and AB
PROOF We know that an angle in a semicircle measures `90^(@)`.
`:. /_ ABC =90^(@) ` and `/_ ABD = 90^(@)`
`implies /_ABC +/_ABD = 90^(@)+90^(@) =180^(@)`
`implies ` CBD is a striaght line
`implies `Points C,B,D are collinear.