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Circles

Circles. Vocabulary And Properties. Circle. A set of all points in a plane at a given distance (radius) from a given point (center) in the plane. r. . center. Radius. A segment from a point on the circle to the center of the circle. r. . Congruent Circles.

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Circles

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  1. Circles Vocabulary And Properties

  2. Circle A set of all points in a plane at a given distance (radius) from a given point (center) in the plane. r  center

  3. Radius A segment from a point on the circle to the center of the circle. r 

  4. Congruent Circles Two circles whose radii have the same measure. r =3 cm r =3 cm

  5. Concentric Circles Two or more circles that share the same center. . 

  6. Chord A segment whose endpoints lie on the circle. Segments AB & CD are chords of G B A  G D C

  7. Diameter A chord passing through the center of a circle. Segment IJ is a diameter of G J  G I

  8. Secant A line that passes through two points of the circle. A line that contains a chord.

  9. Tangent A line in the plane of the circle that intersects the circle in exactly one point. ●  ● The point of contact is called the Point of Tangency

  10. Semicircle A semicircle is an arc of a circle whose endpoints are the endpoints of the diameter. C ● Three letters are required to name a semicircle: the endpoints and one point it passes through.  B A is a semicircle

  11. Minor Arc An arc of a circle that is smaller than a semicircle. C ● Two letters are required to name a minor arc: the endpoints. P  B PC or CB are minor arcs

  12. Major Arc An arc of a circle that is larger than a semicircle. C ●  B A ABC or CAB are major arcs

  13. Inscribed Angle An angle whose vertex lies on a circle and whose sides contain chords of a circle. A C B D <ABC & <BCD are inscribed angles

  14. Central Angle An angle whose vertex is the center of the circle and sides are radii of the circle. A B  K <AKB is a central angle

  15. Properties of Circles The measure of a central angle is two times the measure of the inscribed angle that intercepts the same arc. B A 2x P x C m<APB = 2 times m<ACB ½ m<APB = m<ACB

  16. If the m<C is 55, then the m<O is 110. Both angle C and angle O intercept the same arc, AB. Example B A 110° O 55° C

  17. Angles inscribed in the same arc are congruent. The m<AQB =m<APB both intercept arc AB. A B Q P m<QAP = m<PBQ Both angles intercept QP

  18. Every angle inscribed in a semicircle is an right angle.

  19. Each of the three angles inscribed in the semicircle is a right angle. Example C D B Angle B, C, and D are all 90 degree angles. A E

  20. Property #4 The opposite angles of a quadrilateral inscribed in a circle are supplementary.

  21. Example The measure of angle D + angle B=180 The measure of angle C+angle A=180 B 65 A 70 110 C 115 D

  22. Property #5 Parallel lines intercept congruent arcs on a circle.

  23. Example Arc AB is congruent to Arc CD A B D C

  24. Formulas What are the two formulas for finding circumference? C= C=

  25. Answer C=2 pi r C=d pi

  26. Area of a circle A=?

  27. Answer A=radius square times pi

  28. The End Core-Plus Mathematics Project Home Math Department Home SAHS Home

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