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Getting To PC With A Circle (Posted on 2007-11-10) Difficulty: 2 of 5
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.

See The Solution Submitted by K Sengupta    
Rating: 1.0000 (1 votes)

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Solution Solution | Comment 1 of 9

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
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