# Circles - Algebra Worksheet

Algebra 2
4.1 Notes
4.1 Circles
Date: ___________
Circle:
a set of points in a plane that are a fixed distance, called the ________________, from a given
point, called the __________________.
Learning Target A: I know the standard form for the equation of a circle.
The coordinate plane shows a circle with center C(h, k) and radius, r. P(x, y) is an arbitrary point on
the circle but is not directly above or below or to the left or right of C. A(x, k) is a point with the
same x-coordinate as P and the same y-coordinate as C. Explain why Δ������ is a right triangle.
Identify the lengths of the sides of Δ������. Remember that point P is arbitrary, so you cannot rely
upon the diagram to know whether the x-coordinate of P is greater than or less than h or whether
the y-coordinate is greater than or less than k, so you must use absolute value for lengths of the legs
of Δ������. Also, remember that the length of the hypotenuse of Δ������ is just the radius of the circle.
Length of segment AC = _________________
Length of segment AP = _________________
Length of segment CP = __________________
Apply the Pythagorean Theorem to Δ������ to obtain the equation of the circle.