Presentation top top theme: "Circle Is the set of all points equidistant native a given suggest called the center. The guy is the facility of the circle produced by the shark."— Presentation transcript:




You are watching: The set of all points is called

1 one Is the set of all points equidistant indigenous a given suggest called the center. The guy is the center of the circle created by the shark.

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2 Parts the a circle us name a circle utilizing its center point.⊙ W is shown W• So, the facility is identified as the allude inside the one equidistant from every points on the circle.

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3 Diameter:. Any type of line segment (chord) that contains the circle’s centerDiameter: any kind of line segment (chord) that includes the circle’s center. It is in (ALL diameters the a given circle room  ) Radius: any line segment with 1 endpoint at the center of the circle, and also the other endpoint ~ above the circle. XF (The Radius is = ½ diameter. All radii of a provided circle room ) XF  XE  XB B . . X .E F

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4 Chord: any line segment v endpoints the lie ~ above the circleChord: any type of line segment with endpoints the lie top top the circle. CD Secant: any type of line the intersects the one in specifically 2 clues (cuts through). CD Tangent: Line, segment or beam that intersects the one in precisely 1 suggest (touches) YA or YA constantly perpendicular come radius v endpoint at allude of tangency. XA  YA C. Y . .D . X A .

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5 Arcs – minor arc (less 보다 ½ the circle) abdominal muscle MB YXAArcs – young arc (less than ½ the circle) abdominal muscle MB YXA major arc (at least fifty percent the circle) BMY BAM XYB ar - area developed by 2 radii and the arc created by lock (green area) – favor a slice of pizza. M C E Y B X A

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6 angle in a circle main angle: facility of circle as vertex and also radii together sides.  ACB inscribed angle: vertex suggest on the circle and also chords together sides.  AMB Exterior angle: vertex external the circle, either secants or tangents as sides.  E or  AEB interior angle: peak is intersection of 2 chords inside the circle (not the center).  AWB m  ACB = m abdominal m  AEB = ½(m ab – m XY) m  AMB = ½ m abdominal m  AWB = ½ (m abdominal + m MY) M C E Y W B X A

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7 SEGMENT Lengths in a circle Exterior angle develops inverse proportions (SEGMENT Lengths in a one Exterior angle forms inverse proportions (* note ORDER) PR = PS PR • PQ = PT • PS PT PQ ns S T Q R

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8 SEGMENT Lengths in a circle pertained to chords, secants and tangents Exterior angles kind proportions (* note ORDER) FG = FJ FG • FH = FJ • FJ FJ FH F G H J

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9 SEGMENT Lengths in a circle related to chords, secants and also tangents inner angles form proportions (* note ORDER) be = AE it is in • ED = AE • BC EC ED A D E B C

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10 Postulates and theorems about circlesThe measure of one arc developed by two surrounding arcs is the amount of the measures of the two arcs. In the exact same or congruent circles, two minor arcs space congruent if and also only if their corresponding chords room congruent.

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11 Postulates and theorems around circlesIf a diameter of a one is perpendicular come a chord, climate the diameter bisects the chord and its arc. If one chord is perpendicular bisector of one more chord climate the very first chord is a diameter. In the very same or congruent circles, 2 chords are congruent if and also only if they space equidistant native the center.

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12 Postulates and also theorems around circlesIf an angle is inscriptions in a circle, then its measure up is fifty percent the measure of that is intercepted arc. If two inscribed angles of a circle intercept the very same arc, climate the angles space congruent. A quadrilateral have the right to be inscriptions in a one if and only if its the opposite angles are supplementary.

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13 Postulates and also theorems around circlesIf a tangent and a chord intersect at a suggest on a circle, climate the measure up of every angle created is one fifty percent the measure of that is intercepted arc. If 2 chords intersect in the internal of a circle, climate the measure up of every angle is one half the amount of the steps of the arcs intercepted by the angle and its vertical angle. If a tangent and a secant, two tangents, or two secants crossing in the exterior that a circle, then the measure of the angle created is one fifty percent the distinction of the actions of the intercepted arcs.

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14 Postulates and theorems around circlesIf 2 chords crossing in the interior of a circle climate the product the the lengths the the segments of one chord is same to the p;product that the lengths that the segment of the other chord. If two secant segments share the very same endpoint external a circle, then the product that the length of one secant segment and the length of its outside segment equates to the product the the length of the various other secant segment and the size of its external segment.

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15 Postulates and also theorems around circlesIf a secant segment and also a tangent segment re-publishing an endpoint outside a circle, then the product the the length of the secant segment and the length of its outside segment equates to the square that the length of the tangent segment.

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16 Postulates and also theorems around circlesIn a one of radius r, an arc of degree measure m has actually arc length equal come (m/360 • 2πr). In a circle of radius r, wherein a sector has actually an arc level measure of m, the area the the sector is (m/360 • πr2) The area of a circle is πr2 The one of a one is 2πr

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