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Geometry Chapter 9 The following is a list of items you need to know for the test. circle concentric circles and spheres center inscribed polygons / circumscribed circles chord radius inscribed circles / circumscribed polygons chord common tangents diameter secant tangent circles diameter central angles radius secant tangent minor arc point of tangency major arc sphere semicircle tangent congruent circles inscribed angles Theorems If a line is tangent to a circle, then the line is to the radius drawn to the point of tangency. If a line is to a radius at its outer endpoint, then the line is tangent to the circle. Minor arcs are if and only if their central angles are . In the same circle or in circles: (1) arcs have chords. (2) chords have arcs. A diameter that is to a chord, bisects the chord and its arc. In the same circle or in circles: (1) chords equally distant from the center are . (2) chords are equally distant form the center. An inscribed = ½ its intercepted arc. The formed by a chord and a tangent = ½ its intercepted arc. The formed by 2 chords that intersect inside a circle = ½ the sum of the intercepted arcs. The formed by 2 secants, 2 tangents, or a secant and a tangent = ½ the difference of the intercepted arcs. When 2 chords intersect inside a circle, the product of the segments of 1 chord = the product of the segments of the other chord. (part X part = part X part) The product of one secant and its external segment = the product of the other secant and its external segment. (outside X total = outside X total) The product of one secant and its external segment = the square of the tangent. (outside X total = outside X total) Corollaries Tangents to a circle from a point are . If 2 inscribed s intercept the same arc, then the angles are . An inscribed in a semicircle is a right . If a quadrilateral is inscribed in a semicircle, then its opposite s are supplementary. 1 O1 k m1 k k 1 m1 k 1 k 2 m1 c k b 1 d a j 1 (k j) 2 a b cd m1 1 k 2 s e j 1 c k t k j t k j 1 q s r 1 (k j) 2 es cr m1 1 e m1 1 (k j) 2 tq m1 j 180 m1 1 (k j) 2 es t2