Power of a Point Theorem/Introductory Problem 4
From AoPSWiki
Problem
(ARML) Chords 
and 
of a given circle are perpendicular to each other and intersect at a right angle. 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.
