Consider a circle O with a diameter AB, shown here in green. Draw a second circle (red) with diameter AC, such that C is on AB. Draw an isosceles triangle with base CB and third vertex D on circle O. Draw a third circle (X), tangent to the first three figures. Prove that the line from C to the center of circle X is perpendicular to AB.

(In reply to

Tan by Nithin)

Yes but you must show that the line from C tangent to the red circle passes through circle X. You haven't proved anything meaningful in your post.