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Geometry: Unit 9 Review of Circles S9.1 S9.2 S9.3 I can identify pieces of circles Circle: The set of ALL points (an infinite number) that are the same distance away from a central point That distance is referred to as the radius Chord: a line segment with endpoints on the circle Diameter: the longest possible chord, runs through the center Tangent: a line segment, line or ray that intersects a circle exactly once Secant: a line segment, line or ray that intersects a circle exactly twice I can solve problems involving central & inscribed angles and their intercepted arcs Central angle o An angle formed with its vertex on the center of the circle Is equal to the measure of the intercepted arc it creates Inscribed angle o An angle formed with its vertex on the edge of the circle Is equal to half either the central angle or the intercepted arc I can solve problems involving intersecting chords and the arcs, angles and segments created Chords o cut each other into 2 pieces each product of the pieces is equal o Create a pair of interior vertical angles, which create 2 unequal intercepted arcs The angle is half the sum of the arcs Geometry: Unit 9 Review of Circles S9.1 S9.2 S9.3 I can identify pieces of circles Circle: The set of ALL points (an infinite number) that are the same distance away from a central point That distance is referred to as the radius Chord: a line segment with endpoints on the circle Diameter: the longest possible chord, runs through the center Tangent: a line segment, line or ray that intersects a circle exactly once Secant: a line segment, line or ray that intersects a circle exactly twice I can solve problems involving central & inscribed angles and their intercepted arcs Central angle o An angle formed with its vertex on the center of the circle Is equal to the measure of the intercepted arc it creates Inscribed angle o An angle formed with its vertex on the edge of the circle Is equal to half either the central angle or the intercepted arc I can solve problems involving intersecting chords and the arcs, angles and segments created Chords o cut each other into 2 pieces each product of the pieces is equal o Create a pair of interior vertical angles, which create 2 unequal intercepted arcs The angle is half the sum of the arcs Geometry: Unit 9 Review of Circles S9.4 S9.5 S9.7 I can solve problems involving intersecting tangents and the arcs, angles and segments created Tangents o Tangent is perpendicular to radius at point of tangency o Distance from point of tangency to point of intersection for 2 tangents to the same circle is equal o Line connecting point of intersection to center of circle is bisector (creates a kite) I can solve problems involving intersecting secants and the arcs, angles and segments created Secants o Intersect outside the circle to create an exterior angle and two unequal intercepted arcs The angle is half the difference of the arcs I can solve problems involving proportions in circles (arc length & sector area) Geometry: Unit 9 Review of Circles S9.4 S9.5 S9.7 I can solve problems involving intersecting tangents and the arcs, angles and segments created Tangents o Tangent is perpendicular to radius at point of tangency o Distance from point of tangency to point of intersection for 2 tangents to the same circle is equal o Line connecting point of intersection to center of circle is bisector (creates a kite) I can solve problems involving intersecting secants and the arcs, angles and segments created Secants o Intersect outside the circle to create an exterior angle and two unequal intercepted arcs The angle is half the difference of the arcs I can solve problems involving proportions in circles (arc length & sector area) Area/Perimeter o 𝐴 = 𝜋𝑟 2 o 𝑃𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟 = 𝐶𝑖𝑟𝑐𝑢𝑚𝑓𝑒𝑟𝑒𝑛𝑐𝑒 = 2𝜋𝑟 Area/Perimeter o 𝐴 = 𝜋𝑟 2 o 𝑃𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟 = 𝐶𝑖𝑟𝑐𝑢𝑚𝑓𝑒𝑟𝑒𝑛𝑐𝑒 = 2𝜋𝑟 Proportions Proportions o 𝑝𝑎𝑟𝑡 𝑤ℎ𝑜𝑙𝑒 o 𝑎𝑟𝑐 𝑚𝑒𝑎𝑠𝑢𝑟𝑒 360𝑜 o 𝑐𝑒𝑛𝑡𝑟𝑎𝑙 𝑎𝑛𝑔𝑙𝑒 360𝑜 = 𝑝𝑎𝑟𝑡 𝑤ℎ𝑜𝑙𝑒 = 𝑎𝑟𝑐 𝑙𝑒𝑛𝑔𝑡ℎ 𝐶𝑖𝑟𝑐𝑢𝑚𝑓𝑒𝑟𝑒𝑛𝑐𝑒 = 𝑠𝑒𝑐𝑡𝑜𝑟 𝑎𝑟𝑒𝑎 𝐴𝑟𝑒𝑎 o 𝑝𝑎𝑟𝑡 𝑤ℎ𝑜𝑙𝑒 o 𝑎𝑟𝑐 𝑚𝑒𝑎𝑠𝑢𝑟𝑒 360𝑜 o 𝑐𝑒𝑛𝑡𝑟𝑎𝑙 𝑎𝑛𝑔𝑙𝑒 360𝑜 = 𝑝𝑎𝑟𝑡 𝑤ℎ𝑜𝑙𝑒 = 𝑎𝑟𝑐 𝑙𝑒𝑛𝑔𝑡ℎ 𝐶𝑖𝑟𝑐𝑢𝑚𝑓𝑒𝑟𝑒𝑛𝑐𝑒 = 𝑠𝑒𝑐𝑡𝑜𝑟 𝑎𝑟𝑒𝑎 𝐴𝑟𝑒𝑎