Power of a Point Theorem/Introductory Problem 1

Revision as of 14:15, 23 March 2020 by Coltsfan10 (talk | contribs) (Solution)

Problem

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

Popprob1.PNG

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 $x=\fbox{\textbf{2}}$.

Back to the Power of a Point Theorem.