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Understanding Chord and Secant Intersections in Circles

This session explores the properties and calculations related to intersecting chords, secants, and tangents in circles. Learn how to find the measures of angles formed by two chords that intersect inside a circle and those that intersect outside. Through several examples, you'll master the formulas for solving for unknown variables in various scenarios, ensuring a clear understanding of the relationships between segments. This guide includes practice problems to solidify your learning on chord and secant properties.

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Understanding Chord and Secant Intersections in Circles

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Presentation Transcript

  1. C A B 1 X 222º D Z 55º Session 71 WARM UP 2. Find m1 1. Find mXAB 42º 90º 3. Find mZ 70º

  2. Two chords intersect INSIDE the circle Type 1: a ab = cd d c b

  3. Example 1: 9 12 6 3 x x 2 2 X = 3 X = 8 x 3 6 2 X = 1

  4. 12 2x 8 3x Example 2: Find x 2x  3x = 12  8 6x2 = 96 x2 = 16 x = 4

  5. Two secents intersect OUTSIDE the circle Type 2: E A B C D EA * EB = EC * ED

  6. Example 3: B 13 A 7 E 4 C x D 7 (7 + 13) = 4 (4 + x) x = 31 140 = 16 + 4x 124 = 4x

  7. Example 4: B x A 5 D 8 C 6 E 5 (5 + x) = 6 (6 + 8) x = 11.8 25+5x = 84 59 = 5x

  8. Notice that on the tangent segment, the outside is the whole! Secant Segment External Segment Tangent Segment

  9. Type 2 (with a twist): Secant and Tangent C B E A EA2= EB * EC

  10. Example 5: C B x 12 E 24 A (12 + x) 242 = 12 576 = 144 + 12x x = 36

  11. Example 6: 5 B E 15 C x A (5 + 15) x2 = 5 x2 = 100 x = 10

  12. What you should know by now…

  13. Practice P 220 2-18 even

  14. W.S 10-5

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