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### 38 Cards in this Set

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 the intersection of a sphere with a plane through its center is a circle with the _____ center and ____ radius same A line perpendicular to a radius at its outer end is a tangent to a circle Every tangent is ___ to a radius drawn to the point of contact perpendicular the perpendicular from the center of a circle ___ the chord bisects the chord the segment from the center of a circle to the midpoint of a circle (not diameter) is perpendicular to the chord in the lane of a circle, the perpendicular bisector of a chord passes through the center In the same circle or in conguent circles, any two congruent chords are equidistant from the center. the line-circle theorem if a line and a circle are coplanar and the line intersects the circle, the intersection of the circle is two and only two points a plane perpendiuclar to a radius at its outer end is tangent to the sphere Every tangent plane to a sphere is perpendicular to the radius drawn to the point of contact. If a plane intersects the interior of a sphere, the intersection of the palen and the sphere is a circle. The center o this circle is the foot of the perpendicular from the center of the sphere to the plane. the perpendicular from the center of a sphere to a chord bisects the chord. the segment from the center of a sophere to a chord bisects the chord the segment from the center of a sphere to a midpoint of a chord is perpendicular to the chord The arc addition theorem you can add arcs inscribed angle theorem measure of inscribed angle is half the intercepted arc in same or congruent circles, if two chords are congruent then so are the corresponding minor arcs if two arcs are congruent then so are the corresponding chords tangent-secant theorem given an angle with its vertex on a circle formed by the secant ray and a tangent ray. The measure of the angle is half the measure of the intercepted arc the two tangent theorem the two tangent segments to a circle from a point of the exterior are congruent and determine congruent angels with the segment from the exterior point to the center. The two-secant power theorem outside segment x whole= outside segment x whole *given two secants intersection a circle* the tangent-secant power theorem the segment outside, x the whole= tangent segment^2 the two-chord power theorem let there be two chords, the two segments multiplied= the two segments of the other chord. Unlike rest, no need the "whole segment" anymore. angles inscribed in semicircles are always right if two arcs have equal radii their lengths are proportional to their measures the area of a sector (whilst knowing the length) is A=1/2rL area is half the product of the radius and length of arc. given an apothem and the perimeter of the polyon the area is 1/2 product of perimeter and apothem. the measure of an angle in a polygon is 180- 360/n (n being the # of sides, that is) the measure of an exterior angle of a polygon is 360/n. if 180-360/n holds, to find the exterior, you'd say 180-360/n=180-n (because "n" would be the interior) and obviously it cancels out. given two chords, the measure of an angle formed by the chord is 1/2 the sum of the two intercepted arcs given two lines that forms an angle in the exterior of the circle, the angle of that is 1/2 the difference of the two arcs it intercepts. convex. if you take any two points and connect it, and the line lies in the interior of the polygon it is convex, if not, it's concave. regular polygon: it is regular if it is convex, all the sides are congruent and all angles are congruent. apothem distance from the center of a regular polygon to each of the sides is called the apothem of the polygon. circular region is the union of a circle and its interior inscribed when the vertices of the polygon lies on the circle circumsribed when the polygon is tangent to the circle the ratio of the area of two similar polygons (triangle)is the ratio of their sides, squared.