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.

Join XY and extend it to intersect the circle at points A and B.
Draw a line perpendicular to XY from C to intersect XY at Q.
XA = d-r
XB = d+r
We know that XA.XB = XP²
=> XP = √(d²-r²)
Using similar triangles QYP and XYP
PQ/PY = XP/XY
=> PQ = r*√(d²-r²)/d

PC = 2*PQ = 2r*√(d²-r²)/d

Posted by Praneeth on 2007-11-12 02:53:31