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.

(In reply to Solution by Brian Smith)

I did it a similar way to this. Consider the kite. If you flip one of the triangles, it becomes a rectangle (because the tangent makes a right angle with the radius) So the area of the kite is r*s (where s is the other side), but also note that since the two triangular halves of the kite are congruent, XY forms a right angle with PC. So one can also note the area of the kite equals the sum of the two triangles, or (XY*PC)/2.

So r*s=(XY*PC)/2 implies PC=2*r*s/XY. Substituting sqrt(d^2-r^2) for s and d for XY, one gets 2*r*s/d.

Posted by Gamer on 2007-11-11 02:35:15