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 Getting To PC With A Circle (Posted on 2007-11-10)
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 | 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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