Two circle intersect in `Aa n dBa n dA Ca n dA D` are respectively the diameters of the circles. Prove that `C , B , D` are collinear.

Explanation

Given: Two circle intersect in `A` and `B` and `AC` and `AD` are respectively the diameters of the circles.
To prove: Points `C`, `B` and `D` are colinear.
Proof: `AC` is diameter and point `B` lies on the circumference of the circle
`therefore angleCBA= 90^@`………..(1)[ Angle in a semi circle is `90^@`]
Similarly,
`angleDBA=90^@`…………(2)
Adding equation (1)&(2), we get:
`angleCBA+angleDBA=180^@`
`angleCBD=180^@`
`therefore` The points `C` , `B` and `D` are colinear.
Hence Proved.