Y is the center of a circle having radius r. Point X is located outside the circle and tangents XP and XC are drawn to touch the circle respectively at P and C.

Given that XY = d, determine the length of PC in terms of r and d.

From triangle YPX,

  |YX|^2 = |YP|^2 + |PX|^2

         or

  |PX| = sqrt(d^2 - r^2)              (1)

YPXC is cyclic. Therfore,

  |PC||YX| = |YP||CX| + |YC||PX| = 2|YP||PX|

           or

          2r|PX|
  |PC| = --------                     (2)
            d

Combining (1) and (2),

          2r*sqrt(d^2 - r^2)
  |PC| = --------------------                    
                  d

Posted by Bractals on 2007-11-10 20:40:18