Circles. The student uses the process skills to understand geometric relationships and apply theorems and equations about circles.

G.12.AApply theorems about circles, including relationships among angles, radii, chords, tangents, and secants, to solve non-contextual problems.G.12.BApply the proportional relationship between the measure of an arc length of a circle and the circumference of the circle to solve problems.G.12.CApply the proportional relationship between the measure of the area of a sector of a circle and the area of the circle to solve problems.G.12.DDescribe radian measure of an angle as the ratio of the length of an arc intercepted by a central angle and the radius of the circle.G.12.EShow that the equation of a circle with center at the origin and radius r is x^2 + y^2 = r^2 and determine the equation for the graph of a circle with radius r and center (h, k), (x - h)^2 + (y - k)^2 =r^2.
Example Problems
A circle is centered at and has a radius of .
Where does the point
lie: inside the circle, on the circle, or outside the circle?
A circle is centered at and has a radius of .
Where does the point
lie: inside the circle, on the circle, or outside the circle?
A circle is centered at . The point is on the circle.
Where does the point
lie: inside the circle, on the circle, or outside the circle?
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