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Section 9-1 Circles Vocab

Section 9-1 Circles Vocab. A circle is named by its center point. For example: Circle A or A. Circle – the set of all points in a plane a given distance away from a center point. A. Radius (r). Plural: Radii.

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Section 9-1 Circles Vocab

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  1. Section 9-1 Circles Vocab

  2. A circle is named by its center point. For example: Circle A or A. Circle – the set of all points in a plane a given distance away from a center point. A Radius (r) Plural: Radii Radius – the “given distance away from the center point” of a circle; a segment that joins the center to a point on the circle.

  3. Sphere – the set of all points a given distance away from a center point.

  4. Chord – a segment whose endpoints lie on on the circle. Example: DC A B Diameter – a chord that passes through the center of the circle. Example: AB A diameter is twice the length of a radius. C D

  5. Example: AB Secant – a line that contains a chord. B A **Note: A chord and a secant can be named using the same letters. The notation tells you whether it is a secant or a chord. A secant is a line; a chord is a segment.** Secant: AB Chord: AB

  6. Example: AB Tangent – a line that intersects a circle at exactly one point. Not a tangent! B The point at which the circle and the tangent intersect is called the point of tangency. Example: A A

  7. Congruent Circles – circles with congruent radii. 5cm 5cm Concentric Circles – circles with the same center point.

  8. When each vertex of a polygon is on the circle, the circle is said to be circumscribed around the polygon. This circle is circumscribed around the pentagon

  9. When each side of a polygon is tangent to a circle, the circle is said to be inscribed in the polygon. This circle is inscribed inside of the pentagon.

  10. Section 9-2 Tangents

  11. If AB is tangent to Circle Q at point C, then QC ^ AB. Theorem 9-1: If a line is tangent to a circle, then the line is perpendicular to the radius drawn to the point of tangency. Q is the center of the circle. C is a point of tangency. Q A C B

  12. Example: Given Circle Q with a radius length of 7. D is a point of tangency. DF = 24, find the length of QF. Q 7 D 24 F 72 + 242 = QF2 QF = 25 G NOTE: G is NOT necessarily the midpoint of QF!! Extension: Find GF. GF = 18 QF = 25 QG = 7

  13. Theorem 9-2: If a line in the plane of a circle is perpendicular to a radius at its outer endpoint, then the line is tangent to the circle. This is the converse of Theorem 9-1.

  14. Tangent Circles – coplanar circles that are tangent to the same line at the same point. Internally Tangent Circles Externally Tangent Circles

  15. Common Tangent – a line that is tangent to two coplanar circles. Common Internal Tangent Intersects the segment joining the centers.

  16. Common External Tangent Does not intersect the segment joining the centers.

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