G-C: Geometry: Circles (G-C)

Geometry: Circles (G-C)

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G-C.1Prove that all circles are similar.G-C.2Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle.G-C.3Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.G-C.4Construct a tangent line from a point outside a given circle to the circle.G-C.5Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.
Example Problems
The diameter of a circle is units.
What is the
radius of the circle?
Convert the angle to radians.
Express your answer exactly.
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