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c i r c l e s

c i r c l e s. PARTS OF A CIRCLE Diann Vic B. Torres Angelie B. Butalid Valenrose N. Basera August 23, 2012. Definitions:. CIRCLE – is the set of all points on a plane at a given distance from a fixed point called the center .

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c i r c l e s

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  1. circles PARTS OF A CIRCLE Diann Vic B. Torres Angelie B. Butalid Valenrose N. Basera August 23, 2012

  2. Definitions: • CIRCLE – is the set of all points on a plane at a given distance from a fixed point called the center. • RADIUS - is a segment joining the center to any point on the circle. • CHORD – is a segment joining any two points on the circle. • DIAMETER – is a chord passing through the center.

  3. circle A B D diameter .A C radius center chord F E

  4. Two circles are equal if they have equal radii. 1.5 in 1.5 in A B = CIRCLE A CIRCLE B

  5. THEOREM 8.1 : The segment from the center perpendicular to a chord bisects the chord. B .O D OB AB ┴ A

  6. THEOREM 8.2 : The segment from the center to the midpoint of a chord is perpendicular to the chord. O AD = DB ││ ││ A D B

  7. COROLLARY 8.3 : The perpendicular bisector of a chord passes through the center of the circle. F XY is the perpendicular bisector of EF, ││ X O Y then XY will pass through the center O. ││ E

  8. Theorem 8.4 : If two chords of a circle or of equal circles are equal, then they have the same distance to the center. A Q E Y B Z O. C X F or OE=OF OE=QZ D

  9. Theorem 8.5 : If two chords of a circle or of equal circles have the same distance to the center, then they are equal. A Q Y E Z C O. B X F AB=CD or AB=XY D

  10. A B A polygon is inscribed in a circle if all its vertices are on the circle. The circle is said to be circumscribed about the polygon. .O E C D • ABCDE is inscribed in a circle O. • Circle O is circumscribed about ABCDE.

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