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# Geo ints unit 10

### unit 10 test theorems and postulates

TermDefinition
concentric circles sphere(s) whose centers are the same point
minor arcs measure of a minor arc equals the measure of the corresponding central angle
Arc Addition Postulate the measure of the arc formed by two adjacent arcs is the sum of the measure of the two arcs
theorem 9-3 in the same circle (or congruent circles) two minor arcs are congruent if and only if their central angles are congruent
inscribed angle an angle whose vertex is ON the circle and whose sides are chords of the circle
theorem 9-7 the measure of an inscribed angle is equal to half the measure of its intercepted arc
corollary to the inscribed angle theorem if two inscribed angles intercept the same arc (or congruent arcs) then the angles are congruent
corollary 2 an angle inscribed in a semicircle is a right angle
corollary 3 if a quadrilateral is inscribed in a circle, then its opposite angles are supplementary
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
corollary to thm 9-1 and 9-2 tangents to a circle from (the same) point are congruent
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
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
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
theorem 9-10 (case 2) the angle formed by a tangent and a secant is half the difference of the intercepted arcs
theorem 9-10 (case 3) the angle formed by two tangents is half the difference of the intercepted arcs
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)
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)
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)
Created by: mtwhitneygirl