Curriculum / Math / 10th Grade / Unit 7: Circles / Lesson 12
Math
Unit 7
10th Grade
Lesson 12 of 14
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Describe the proportional relationship between arc length and the radius of a circle. Convert between degrees and radians to write the arc measure in radians.
Topic A: Equations of Circles
Derive the equation of a circle using the Pythagorean Theorem where the center of the circle is at the origin.
Standards
G.GPE.A.1G.GPE.B.4
Given a circle with a center translated from the origin, write the equation of the circle and describe its features.
G.C.A.1G.CO.A.5G.GPE.A.1
Write an equation for a circle in standard form by completing the square. Describe the transformations of a circle.
G.CO.A.5G.GPE.A.1
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Topic B: Angle and Segment Relationships in Inscribed and Circumscribed Figures
Define a chord to derive the Chord Central Angles Conjecture and Thales’ Theorem.
G.C.A.2
Describe the relationship between inscribed and central angles in terms of their intercepted arc.
Determine the angle and length relationships between intersecting chords.
Prove properties of angles in a quadrilateral inscribed in a circle.
G.C.A.3
Define and determine properties of tangents and secants of circles to solve problems with inscribed and circumscribed triangles.
G.C.A.2G.C.A.3
Construct tangent lines to a circle to define and describe the circumscribed angle.
G.C.A.2G.C.A.4
Use angle and side length relationships with chords, tangents, inscribed angles, and circumscribed angles to solve problems.
Topic C: Arc Length, Radians, and Sector Area
Define, describe, and calculate arc length.
G.C.B.5
Calculate the sector area of a circle. Identify relationships between sector area, arc angle, and radius.
Use sector area of circles to calculate the composite area of figures.
G.C.B.5N.Q.A.2N.Q.A.3
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