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Parts of a Circle

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Taryn Ackelson

on 22 February 2014

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Transcript of Parts of a Circle


Center Point
Radius - Radii
Diameter
Chord
Secant
Tangent
Central Angle
Inscribed Angle
Intersected Arc
Arc major arc - minor arc - semicircle
Theorem --- A line is a tangent if and only if the line is perpendicular to a radius of the circle
Common tangents can be internal or external
The difference is that internal tangents cross through a line that can be drawn from the center of the circle.
Theorem
Tangent Segments from a common external point are congruent
This will be important for the section on special segments
ARCS
Minor Arcs are named with 2 letters, the endpoints, and they lie on the circle. The minor arc is equal to the central angle that shares its endpoints. The sides of the angle that "cuts" a minor arc are radii.

Major Arcs are named with 3 letters, the endpoints and one point on the circle that is between them. This gives reference for the direction you travel to determine the arc's position. They are also 180 degrees of larger. The major arc is equal to 360 - the minor arc.

Semicircles = 180 degrees and are formed by any diameter of a circle. They are named with 3 letters.
Chords
See Theorems 10.3, 10.4, 10.5, 10.6 of the SHS Geometry Book pages 664-666

These four theorems talk about what makes two chords congruent in the same circle or congruent circles.
10.3 of the book matches the "Chords" section on OdysseyWare


Inscribed Angles
An inscribed angle has a vertex on the circle and two endpoints on the circle. Its two sides contain an arc of the circle, this is the intercepted arc.

THEOREM --- The measure of an inscribed angles is equal to 1/2 the measure of its intercepted arc.

THEOREM --- Two inscribed angles that intercept the same arc have congruent angles.
A little more about inscribed angles....
THEOREM --- A quadrilateral can be inscribed in a circle if and only if its opposite angles are supplementary
The sum of the angles must = 180
Part one: The IMPACT of Circles
Parts of a Circle
Arc addition postulate:
The measure of an arc
formed by two adjacent
arcs is the sum of the
measures of the two arcs
THEOREM ---
A semicircle has an
inscribed angle of
90 degrees
Full transcript