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Circles Concept Map

Justine Baker Period 5
by

Justine Baker

on 5 December 2017

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Transcript of Circles Concept Map

Circle Concept Map
Circles
Basic Parts of a Circle
Types of Angles in a Circle
Pi
Formulas
Other
All Circles are Similar
h
Central Angles
Circles are round
Centroids
Proof
Justine Baker
Period 5

Radius
Diameter
Chord
Tangent
Secant
Inscribed Angles
Created by the angle of two radiuses in a circle
Center
Made with two chords or two secants in a circle
Equal to half of the central angle it shares an arc with
Equal to twice the amount of the inscribed angle it shares an arc with
Formula for Circumference
Sector
Area Formula
The area between two radii and the arc.
A line that passes through a circle at two points.
A line that passes through a circle at one point.
A line segment that begin from the centre and touches any point on the circle.
Point in exact middle where all other points are equidistant away from.
Must pass through the centre of the circle. The Diameter is equal to twice the radius.
The chord joins any two points on a circle.
Arcs
Sections of the circumference
Equal to half of the inscribed angle it is related to or the same as the central angle it is related to
Constructions of a Circle
Circumscribed Constructions
When an object's points all rest on the circle that surrounds it.
Inscribed Construction
To draw a circle within a polygon where the enclosed circle touches the outer figure.
Tangent Construction
When a tangent is created on a circle.
Given a circle of radius r and a second circle of radius R
Dilate with a scale factor of k= R/r
The circles will map onto eachother by a dilation
All circles are similar
When bisected, it has a 90 degree angle with the center.
Relationship with the Diameter
Pi is used to calculate the circumference of a circle along with the diameter.
Relationship with the Radius
Pi is used to calculate the area and circumference with the radius.
Circumcenter
The center of the circle that is circumscribed around the polygon.
Incenter
The center of the circle inside the polygon.
The intersection of all straight lines that divide X.

Theorem=2[4r/3(pi)]
Orthocenter
The intersection of three altitudes.
Radians
A pure measure based on the radius of a circle.

1 Radian is equal to about 57.2958 degrees.
Unit Circle
When a circle has the radius of 1.
The 9-Point Circle
A circle that can come from any triangle that has nine points coming from:

The midpoint of each side
The foot of each altitude
The midpoint of the line segment from each vertex of the triangle and the orthocenter
Full transcript