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Section: G.6.3

Central and inscribed angles

• Identify and describe relationships between central and inscribed angles and their arcs.
• Prove that an inscribed angle that subtends a diameter is a right angle, and, conversely, that a right angle inscribed in a circle must subtend a diameter.
• Apply these relationships in various contexts.

Students begin this unit by working with circles on the coordinate plane and use the Pythagorean Theorem to derive the equation of a circle. They learn about radian measure and use similarity to derive the fact that the length of the arc intercepted by an angle is proportional to the radius of the circle. They develop a formula for the area of a sector of a circle and examine properties of central and inscribed angles in a circle along with their subtended arcs. Students also examine properties of tangent lines, radii, and intersecting chords and apply these properties to solve problems in a variety of contexts, including real-world situations.

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Tasks

1 Orbiting Satellite

2 Right triangles inscribed in circles I

3 Right triangles inscribed in circles II

* The following tasks appear earlier in this file: * Task 33: G-CO Are the Triangles Congruent?