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

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

Latest revision as of 14:15, 23 March 2020

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 $x=\fbox{2}$.

Back to the Power of a Point Theorem.