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,
PCYX = YPCX + YCPX = 2YPPX
or
2rPX
PC =  (2)
d
Combining (1) and (2),
2r*sqrt(d^2  r^2)
PC = 
d

Posted by Bractals
on 20071110 20:40:18 