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Circle Concept Map

Third Quater Geometry honros Project
by

alannah newcomer

on 18 March 2013

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Transcript of Circle Concept Map

Circle Parts of a
circle Width of a circle from the center
point to a point on the edge of
the circle. Radius A straight line going through the center of a circle connecting two points on the circumference. Diameter The diameter is twice the size of the radius Tangent A line which touches a
circle at just one
point. Secant A line that intersects a circle
at two points Chord A straight line connecting two
points on a curve Angle Relationships Inscribed Angle Central Angle Tangent Angle Exterior Angle Radius intercepting
another radius Intercepted Arc Equal to Equal to 1/2 of is twice the Chord intercepting another chord inside a circle Interior Angle Constructions Circumscribed The angle subtended at a point on the circle by
two given points on the circle radius meeting with tangent An angle formed by perpendicular bisecting of the radius and a tangent, so it is always equal to 90 degrees. Angle with its vertex is at the center point of a circle arcs lying between the sides
of the specified angles equal to 1/2 of the sum of Four angles formed inside a circle, whose vertical angles are congruent Two tangents intersecting
outside a circle Two secants intersecting outside a circle A tangent and a secant intersecting outside a circle Angle formed outside of a circle due to intersecting lines Equal to 1/2 of the
difference of Tangent Steps:
•Draw a line connecting the point to the center of the circle
•Construct the perpendicular bisector of that line
•Place the compass on the midpoint, adjust its length to reach the end point, and draw an arc across the circle
•Where the arc crosses the circle will be the tangent points. Process of drawing a tangent line on a circle a circle that passes through all three vertices of a given triangle or through the vertices of a given cyclic polygon Circumcenter The point that is in the center of
the circumscribed circle Inscribed Steps:
•Bisect one of the angles
•Bisect another angle
•Where they cross is the center of the inscribed circle
•Construct a perpendicular from the center point to one side of the triangle
•Place compass on the center point, adjust its length to where the perpendicular crosses the triangle, and draw your inscribed circle! The process of drawing a circle inside of a triangle or other polygon. Incenter the center of the triangle's incircle Arcs A portion of the circumference
of a circle Major/ Minor Arc the major arc is the section that is larger than 180 degrees the minor arc is the section that is less than 180 degrees Adjacent Arcs Non-overlapping arcs with the same radius and center, sharing a common endpoint Intercepted Arc the part of a circle that lies between two lines
that intersect it Equations Basic A circle can be defined as the focus of all points that fit
the equation: x2 + y2 = r2 Center at (0,0) General A circle can be defined as the focus of all points that fit
the equation (x-h)2 + (y-k)2 = r2 Center anywhere Parametric A circle can be defined as the focus of all points that fit
the equations x = r cos(t) y = r sin(t) Pi the ratio of the circumference of a
circle to its diameter Formulas Area Circumference Proofs More! a pure measure based on the Radius of the circle Radians The size of a radian is determined by the requirement that there are
2 radians in a circle Unit Circle a circle with a radius of 1 Sine, Cosine, and Tangent Since the radius is 1, you can directly measure them. Pythagoras When you take Pythagorean theorem, you get the equation of a unit circle x2 + y2 = 1 Nine-Point Circle Steps
-Mark the midpoints of each side
-Drop an altitude from each vertex to the opposite side, and mark the points where the altitudes intersect the opposite side
-Mark the midpoint between each vertex and this common point. A circle drawn through nine specific
points on a triangle All circles are similar This can be proven by setting the two circles on the same center point, then by dilating the circles with
k=radii/radii.
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