Circles and Chords Exploring the relationships between ircumference, diameter, chords, central angles, and inscribed angles. QuickTime™ and a decompressor are needed to see this picture. Photo from: http://www.shpefoundation.org/media/images/Escalante-phot
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Circles and Chords
Exploring the relationships between circumference,
This is a diagram Showing the variousTypes of linesDrawn in relationTo a circle.We will use the Properties of theseLines to determine The measure and Length of arcs and Chords.
What is a chordWhat is an arcRelationships between anglesRelationships between chords and linesHow to find the length of a chordHow to find the measure of an arcHow to find the length of an arc
What is a chord
QuickTime™ and a decompressor
are needed to see this picture.
A line connecting two points on a circle is called a chord. The Chord AB connects the points A and B.
Central angles are the angles running through the center and two points on the circle. They have the same measure as the arcs they intercept.
Intercepted Arc
Relationships between angles continued
Inscribed angles connect an arc to a point on the circle. Any inscribed angles intercepting the same arc have the same angle measure. Inscribed angles are half the measure of the central angle intercepting the same arc.
Angle measures: a = 90˚ b = 90˚ c = 20˚ d = 200˚ e = 60˚ f = 120˚˚
So far we have learned:
What is a chordWhat is an arcRelationships between anglesRelationships between chords and
linesHow to find the length of a chordHow to find the measure of an arcHow to find the length of an arc
QuickTime™ and a decompressor
are needed to see this picture.
QuickTime™ and a decompressor
are needed to see this picture.
QuickTime™ and a decompressor
are needed to see this picture.
Relationships between chords and lines
A diameter can be drawn such that the diameter is a perpindicular bisector of the chord (It cuts the chord in half and the diameter and chord form right angles)
Angles AED and CEB are Vertical angles, and are Congruent. Angles DAB and BCD intersect the same arc And are therefore congruent.So by AA~, triangles DAB andBCD are congruent.
So far we have learned:
What is a chordWhat is an arcRelationships between anglesRelationships between chords and
linesHow to find the length of a chordHow to find the measure of an arcHow to find the length of an arc