Circle

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# Circle - PowerPoint PPT Presentation

Circle. Is the set of all points equidistant from a given point called the center. The man is the center of the circle created by the shark. Parts of a circle. We name a circle using its center point. ⊙ W is shown W •

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## PowerPoint Slideshow about ' Circle' - konane

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Presentation Transcript

### Circle

Is the set of all points equidistant from a given point called the center.

The man is the center of the circle created by the shark.

Parts of a circle

We name a circle using its center point.

⊙ W is shown

W•

So, the Center is defined as the point inside the circle equidistant from all points on the circle.

Diameter: Any line segment (chord) that contains the circle’s center. BE (ALL diameters of a given circle are  )Radius: Any line segment with 1 endpoint at the center of the circle, and the other endpoint ON the circle. XF (The Radius is = ½ diameter. All radii of a given circle are ) XF  XE  XB

B .

. X

.E

F

Chord: Any line segment with endpoints that lie on the circle.CD Secant: Any line that intersects the circle in exactly 2 points (cuts through).CDTangent: Line, segment or ray that intersects the circle in exactly 1 point (touches)YA or YAAlways perpendicular to radius with endpoint at point of tangency. XA  YA

C.

Y .

.D

. X

A .

Arcs – minor arc (less than ½ the circle) AB MB YXA major arc (at least half the circle) BMY BAM XYBSector - area formed by two radii and the arc formed by them (green area) – like a slice of pizza.

M

C

E Y

B

X

A

ANGLES in a circleCentral angle: center of circle as vertex and radii as sides.  ACBInscribed angle: vertex point on the circle and chords as sides.  AMBExterior angle: vertex outside the circle, either secants or tangents as sides.  E or  AEBInterior angle: vertex is intersection of two chords inside the circle (not the center).  AWB

m  ACB = m AB m  AEB = ½(m AB – m XY)

m  AMB = ½ m AB m  AWB = ½ (m AB + m MY)

M

C

E Y W

B

X

A

SEGMENT Lengths in a circleExterior angle forms inverse proportions (* NOTE ORDER)

PR = PS PR • PQ = PT • PS

PT PQ

P

S

T

Q

R

SEGMENT Lengths in a circlerelated to chords, secants and tangentsExterior angles form proportions (* NOTE ORDER)

FG = FJ FG • FH = FJ • FJ

FJ FH

F G H

J

SEGMENT Lengths in a circlerelated to chords, secants and tangentsInterior angles form proportions (* NOTE ORDER)

BE = AE BE • ED = AE • BC

EC ED

A

D

E

B

C

• The measure of an arc formed by two adjacent arcs is the sum of the measures of the two arcs.
• In the same or congruent circles, two minor arcs are congruent if and only if their corresponding chords are congruent.
• If a diameter of a circle is perpendicular to a chord, then the diameter bisects the chord and its arc.
• If one chord is perpendicular bisector of another chord then the first chord is a diameter.
• In the same or congruent circles, two chords are congruent if and only if they are equidistant from the center.
• If an angle is inscribed in a circle, then its measure is half the measure of its intercepted arc.
• If two inscribed angles of a circle intercept the same arc, then the angles are congruent.
• A quadrilateral can be inscribed in a circle if and only if its opposite angles are supplementary.