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.

Think of it this way.

The line AC is the diameter of the Red circle, which continues on to B making it the diameter of the large green circle.

If you extend the line from C in the opposite direction it makes a tangent to the red circle. since the diameter of the green circle and the red circle are on the line AB and the the line from C is a tangent to the circle with the diameter. Thus makin the line extending from C Perpendicular to the line AB.

Posted by Nithin on 2004-09-24 17:18:08