Power of a Point Theorem/Introductory Problem 4
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.