# Find the x coordinate of the point at which the tangent line to a circle centered at the origin intersects the x axis.

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Find the x coordinate of the point at which the tangent line to a circle centered at the origin intersects the x axis.

Consider the circle of radius 4 that's centered at the origin. Let P be a point which is on that circle but not on the y axis, and let Q be the point at which the line tangent to the circle at point P intersects the x axis. Express the x coordinate of Q in terms of the x coordinate of P.

Also, let theta be the angle (measured counterclockwise) whose initial side is the positive x axis and whose terminal side is the ray from the origin that passes through point P. Express the x coordinate of Q in terms of theta.

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##### Solution Summary

All of the pertinent information is reviewed, and the problem is solved step by step and in detail, to find the x coordinate of the point.

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- AB, Hood College
- PhD, The Catholic University of America
- PhD, The University of Maryland at College Park

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