Circles vocab 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 A B D C G
- 7. Diameter A chord passing through the center of a circle. Segment IJ is a diameter of G I J G
- 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. is a semicircle C BA ● ACB Three letters are required to name a semicircle: the endpoints and one point it passes through.
- 11. Minor Arc An arc of a circle that is smaller than a semicircle. P C B ● PC or CB are minor arcs Two letters are required to name a minor arc: the endpoints.
- 12. Major Arc An arc of a circle that is larger than a semicircle. C BA ● 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. B A C 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 K B <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. P A B C m<APB = 2 times m<ACB ½ m<APB = m<ACB x 2x
- 16. Example If the m<C is 55°, then the m<O is 110°. Both angle C and angle O intercept the same arc, AB. O A B C 55° 110°
- 17. Angles inscribed in the same arc are congruent. A Q B P m<QAP = m<PBQ Both angles intercept QP The m<AQB =m<APB both intercept arc AB.
- 18. Every angle inscribed in a semicircle is an right angle.
- 19. Example Each of the three angles inscribed in the semicircle is a right angle. A B C D E Angle B, C, and D are all 90 degree angles.
- 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° A B C D 110 70 115 65
- 22. Property #5 Parallel lines intercept congruent arcs on a circle.
- 23. Example A B Arc AB is congruent to Arc CD C D
- 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 H Math Department Home SAHS Home