# DEPRECATED Pythagorean theorem and the equation of a circle

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### Problem

Circle O has a center at left parenthesis, 1, comma, minus, 4, right parenthesis and a radius of 5.
To derive the equation of this circle, we will use the Pythagorean theorem.
First, we pick any point on the circle and call it A, with coordinates left parenthesis, x, comma, y, right parenthesis. We create a right triangle with hypotenuse start color blue, start overline, O, A, end overline, end color blue and vertex at right angle B.
Use the Pythagorean theorem to find the equation of the circle.
What is the length of start color pink, start overline, O, B, end overline, end color pink ?
What is the length of start color green, start overline, A, B, end overline, end color green ?
Write the equation of the circle.