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Power of a Point Theorem/Introductory Problem 1

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Problem

Find the value of x in the following diagram:

Image:popprob1.PNG

Solution

Applying the Power of a Point Theorem gives us 3\cdot(3+5) = x (x+10). Expanding and simplifying we get x^2 + 10x - 24 = 0. This factors as (x+12)(x-2) = 0. We discard the negative solution since distance must be positive. Thus x=2.

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