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Circle Theorems and Examples

Learn about important theorems related to circles, such as congruent chords and arcs, perpendicular bisectors of chords, and equidistant chords from the center. Practice with examples and sketches for better understanding.

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Circle Theorems and Examples

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  1. Arcs and Chords Lesson 9-4

  2. A B E C D Theorem #1: In a circle, if two chords are congruent then their corresponding minor arcs are congruent. Example:

  3. D B A E C Theorem #2: In a circle, if a diameter (or radius) is perpendicular to a chord, then it bisects the chord and its arc. Example: If AB = 5 cm, find AE.

  4. D F C O B A E Theorem #3: In a circle, two chords are congruent if and only if they are equidistant from the center. Example: If AB = 5 cm, find CD. Since AB = CD, CD = 5 cm.

  5. 15cm A B D 8cm O Try Some Sketches: • Draw a circle with a chord that is 15 inches long and 8 inches from the center of the circle. • Draw a radius so that it forms a right triangle. • How could you find the length of the radius? Solution: ∆ODB is a right triangle and x

  6. A B 10 cm 10 cm O C 20cm D Try Some Sketches: • Draw a circle with a diameter that is 20 cm long. • Draw another chord (parallel to the diameter) that is 14cm long. • Find the distance from the smaller chord to the center of the circle. Solution: ∆EOB is a right triangle. OB (radius) = 10 cm 14 cm E x 7.1 cm

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