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.

Forgive me if I'm wrong...But...It never says that circle x has to lie "above" AB...So...I put circle X "below" AB...So the center of X is in the green space under CB...X is tangent to all three figures, but CX is obviously not perpendicular to AB. I used some MSPaint and fixed up the diagram...You can see my circle and points of tangency, with my CX drawn in. Picture

Posted by Caz on 2005-11-06 22:17:27