Curriculum / Math / 10th Grade / Unit 7: Circles / Lesson 9
Math
Unit 7
10th Grade
Lesson 9 of 14
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Lesson Notes
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Construct tangent lines to a circle to define and describe the circumscribed angle.
The core standards covered in this lesson
G.C.A.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.
G.C.A.4 — Construct a tangent line from a point outside a given circle to the circle.
The foundational standards covered in this lesson
G.CO.D.13 — Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
25-30 minutes
Construct a tangent line to circle $$A$$ at point $$B$$.
Tangent to a Circle at a Point by John D. Page is made available on Math Open Reference. © 2011 Copyright Math Open Reference. All rights reserved. Accessed Sept. 19, 2018, 2:04 p.m..
Below is circle $$A$$ with tangent lines $$\overleftrightarrow{BD}$$ and $$\overleftrightarrow{CD}$$.
What is the relationship between the central angle and the circumscribed angle?
Geometry - 8.9 AP2 by Match Fishtank is made available by GeoGebra under the CC BY-NC-SA 3.0 license. Copyright © International GeoGebra Institute, 2013. Accessed June 13, 2017, 11:49 a.m..
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
5-10 minutes
The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.
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Use angle and side length relationships with chords, tangents, inscribed angles, and circumscribed angles to solve problems.
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
G.C.A.2G.C.A.4
Topic C: Arc Length, Radians, and Sector Area
Define, describe, and calculate arc length.
G.C.B.5
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.
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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