Mathematics II Circles

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Understand and apply theorems about circles.
1. Prove that all circles are similar.
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.
3. Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed
in a circle.
4. (+) Construct a tangent line from a point outside a given circle to the circle.
Find arc lengths and areas of sectors of circles. [Radian introduced only as unit of measure]
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. Convert between