Art of Problem Solving

Power of a Point Theorem/Introductory Problem 1: Difference between revisions

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Revision as of 08:19, 1 July 2006

Problem

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

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 $x=2$.

Back to the Power of a Point Theorem.