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Standards/Math/South Carolina/G.GCI

G.GCI

G Geometry
G.GCI
G.GCI.1G.GCI.2G.GCI.3G.GCI.4G.GCI.5
G.GCO
G.GGMD
G.GGPE
G.GM
G.GMD
G.GSRT
G.SPID

Circles

G.GCI.1Prove that all circles are similar.G.GCI.2Identify and describe relationships among inscribed angles, radii, and chords; among inscribed angles, central angles, and circumscribed angles; and between radii and tangents to circles. Use those relationships to solve mathematical and real-world problems.G.GCI.3Construct the inscribed and circumscribed circles of a triangle using a variety of tools, including a compass, a straightedge, and dynamic geometry software, and prove properties of angles for a quadrilateral inscribed in a circle.G.GCI.4Construct a tangent line to a circle through a point on the circle, and construct a tangent line from a point outside a given circle to the circle; justify the process used for each construction.G.GCI.5Derive the formulas for the length of an arc and the area of a sector in a circle and apply these formulas to solve mathematical and real-world problems.
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