Math Problem Statement
In the graph on the right, a line segment through the center of the circle intersects the circle at the points
(5,5)
and
(7,
15)
as shown.
a. Find the coordinates of the circle's center.
b. Find the radius of the circle.
c. Use your answers from parts (a) and (b) to write the standard form of the circle's equation.
Solution
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Math Problem Analysis
Mathematical Concepts
Geometry
Coordinate Geometry
Circles
Formulas
Midpoint formula: M = ((x1 + x2) / 2, (y1 + y2) / 2)
Distance formula: d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Equation of a circle: (x - h)^2 + (y - k)^2 = r^2
Theorems
Pythagorean Theorem (used in distance formula)
Suitable Grade Level
Grades 9-10
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