Difference between revisions of "Power of a Point Theorem/Introductory Problem 4"
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== Problem == | == Problem == | ||
| − | ([[ARML]]) Chords <math> AB </math> and <math> CD </math> of a given circle are perpendicular to each other and intersect at a right angle. Given that <math> BE = 16, DE = 4, </math> and <math> AD = 5 </math>, find <math> CE </math>. | + | ([[ARML]]) Chords <math> AB </math> and <math> CD </math> of a given circle are perpendicular to each other and intersect at a right angle at <math>E</math> . Given that <math> BE = 16, DE = 4, </math> and <math> AD = 5 </math>, find <math> CE </math>. |
== Solution == | == Solution == | ||
Revision as of 02:25, 20 February 2020
Problem
(ARML) Chords 
and 
of a given circle are perpendicular to each other and intersect at a right angle at 
. Given that 
and 
, find 
.
Solution
is a right triangle with hypotenuse 5 and leg 4. Thus, by the Pythagorean Theorem, 
(or by just knowing your Pythagorean Triples). Applying the Power of a Point Theorem gives 
, or 
. Solving gives 
.
Back to the Power of a Point Theorem.
