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unit 10 test theorems and postulates

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Term
Definition
concentric circles   sphere(s) whose centers are the same point  
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minor arcs   measure of a minor arc equals the measure of the corresponding central angle  
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Arc Addition Postulate   the measure of the arc formed by two adjacent arcs is the sum of the measure of the two arcs  
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theorem 9-3   in the same circle (or congruent circles) two minor arcs are congruent if and only if their central angles are congruent  
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inscribed angle   an angle whose vertex is ON the circle and whose sides are chords of the circle  
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theorem 9-7   the measure of an inscribed angle is equal to half the measure of its intercepted arc  
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corollary to the inscribed angle theorem   if two inscribed angles intercept the same arc (or congruent arcs) then the angles are congruent  
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corollary 2   an angle inscribed in a semicircle is a right angle  
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corollary 3   if a quadrilateral is inscribed in a circle, then its opposite angles are supplementary  
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thm 9-1 and 9-2   a line is tangent to a circle if and only if the line is perpendicular to a radius at the point of tangency  
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corollary to thm 9-1 and 9-2   tangents to a circle from (the same) point are congruent  
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theorem 9-8   the measure of an angle formed by a chord and a tangent is equal to half the measure of the intercepted arc  
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theorem 9-9   the measure of an angle formed by two chords that intersect inside a circle is equal to half the sum of the intercepted arcs  
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theorem 9-10 (case 1)   two secants that meet outside of a circle from an angle is equal to half the difference of the arcs they intercept  
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theorem 9-10 (case 2)   the angle formed by a tangent and a secant is half the difference of the intercepted arcs  
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theorem 9-10 (case 3)   the angle formed by two tangents is half the difference of the intercepted arcs  
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chord-chord power theorem ("power of E")   when two chords intersect inside a circle, the product of the segments of one chord equals the product of the segments of the other chord (pp x pp)  
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secant-secant power theorem (power of "A")   when two secants are drawn to a circle from an external point, the product of one secant segment and its external segment equals the product of the other secant segment and its external segment (OW x OW)  
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Secant-tangent power theorem (thm 9-13)   when a secant segment and a tangent segment are drawn to a circle from an external point, the product of the secant segment and its external segment is equal to the square of the tangent segment (OW x OW)  
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