Examples for

Common Core Math: High School Geometry: Circles

In high school, students define and describe measurements of circles, using terms like radius, diameter, chord and tangent. Students compute arc length and sector area and apply theorems involving central, inscribed and circumscribed angles. Students also use angles to analyze circles and their relationships to other shapes, including by constructing inscribed and circumscribed circles of triangles and quadrilaterals.
Common Core Standards

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CCSS.Math.Content.HSG-C.A.2
hsg.c.b5 common core standard

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common core standards about circles
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Measurements in Circles

Define and compute measurements and properties of circles.

Prove that all circles are similar (CCSS.Math.Content.HSG-C.A.1):

mathematical definition of a circle
circle with radius 2 vs circle with radius 8

Recognize and apply properties of angles in circles (CCSS.Math.Content.HSG-C.A.2):

central angle
inscribed angle
circle tangent line

Find lines tangent to a circle (CCSS.Math.Content.HSG-C.A.4):

line through (3, 3) and tangent to x^2 + y^2 = 1
tangent line to (x + 1)^2 + (y - 3)^2 = 9 through (-5, 6)
line tangent to x^2 + y^2 = 1 at (1/2, sqrt(3)/2)

Compute arc lengths and sector areas (CCSS.Math.Content.HSG-C.B.5):

arc length for r = 3 and 120 degrees
radius 9, 30 deg arc length
arc length for r = 1 and theta = 1 rad
sector area for r = 2 and 45 degrees
radius 0.75, angle Pi/5 sector area
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Inscribed & Circumscribed Circles

Relate circles to other geometric figures.

Inscribe circles within polygons (CCSS.Math.Content.HSG-C.A.3):

3-4-5 triangle with inscribed circle
{{1, 1}, {3, 6}, {9, -2}} triangle incenter

Find circumcircles surrounding polygons (CCSS.Math.Content.HSG-C.A.3):

circumcircle of 2-2-2 triangle
{{0, 7}, {1, 4}, {-5, 3}} triangle circumcenter
unit square circumcircle
cyclic quadrilateral
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