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A line is tangent to a circle at the point (2, 5). A parallel line is tangent to the circle at (8, 13). What is the common slope of the two lines? Express your answer as a common fraction.

May 28, 2018

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Ok, here I go:

To find the slope, we use our trusty formula- $$\frac{y_2-y_1}{x_2-x_1}$$

Plugging in the values, we have:$$\frac{13-5}{8-2}=\frac{8}{6}=\frac{4}{3}$$

But since the two tangents lines are perpendicular to this diameter and have a slope equal to the negative reciprocal of the diameter’s slope, we have $$\boxed{\frac{-3}{4}}$$

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May 28, 2018