Power of a Point Theorem/Introductory Problem 1

Problem

Find the value of $x$ in the following diagram:

Solution

Applying the Power of a Point Theorem, we get $3\cdot(3+5) = x (x+10) \rightarrow x^2 + 10x - 24 = 0$ . This factors as $(x+12)(x-2) = 0$ . We discard the negative solution since distance must be positive. Thus $x=\fbox{2}$ .

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Power of a Point Theorem/Introductory Problem 1

Problem

Solution