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38 Cards in this Set
 Front
 Back
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 linecircle 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


tangentsecant 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 twosecant power theorem

outside segment x whole= outside segment x whole *given two secants intersection a circle*


the tangentsecant power theorem

the segment outside, x the whole= tangent segment^2


the twochord 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 180360/n holds, to find the exterior, you'd say 180360/n=180n (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.
