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HSG-C Circles

Understand and apply theorems about circles

HSG-C.1 Prove that all circles are similar. Aligned Resources

HSG-C.2 Identify 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. Aligned Resources

HSG-C.3 Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle. Aligned Resources

HSG-C.4 (+) Construct a tangent line from a point outside a given circle to the circle. Aligned Resources

Find arc lengths and areas of sectors of circles

HSG-C.5 Derive 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. Aligned Resources