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38 Cards in this Set

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  • 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 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.