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Circle Properties: Area and Circumference Calculation

Learn about circle properties and how to calculate the area and circumference of circles using tangents, radii, chords, and more. Explore definitions and examples.

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Circle Properties: Area and Circumference Calculation

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  1. Do Now • Find the area and circumference of each circle 1) 2)

  2. 10.1 Use Properties of Tangents Objective: To use properties of tangents

  3. Definition of a circle and its center • A circle is the set of all points in a plane that are equidistant from a given point called the center of the circle. Circle B B

  4. Circle Vocabulary • Tangent: A line in the plane of a circle that intersects the circle in exactly one point (the point of tangency).

  5. Circle Vocabulary • Center: C and G • Radius: a segment whose endpoints are the center and any point on the circle. (AC, CD, CH, GE, GF) • Chord: a segment whose endpoints are on a circle. (AB and AD)

  6. Circle Vocabulary • Diameter: a chord that contains the center of the circle. (AD) • Secant: a line that intersects a circle in two points. (AB)

  7. Circle Vocabulary • Common internal tangent: a line that is tangent to two circles & goes between two circles. (tangent HF is internal) • Common external tangent: a line that is tangent to two circles & lies outside both circle. (tangent DE is external)

  8. Example 1: Common Tangents

  9. Theorem • In a plane, a line is tangent to a circle if and only if the line is perpendicular to a radius of the circle at its endpoint on the circle. CB is tangent to circle A at point C which is the point of tangency. This makes CB perpendicular to AC. C B A

  10. Example 2:

  11. Example 3:

  12. Theorem • Tangent segments from a common external point are congruent. C A B

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