# 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.*