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Angle Measures: Chords, Secants, and Tangents

Learn how to find the measures of angles formed by chords, secants, and tangents in a circle using theorems and formulas. Practice examples included.

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Angle Measures: Chords, Secants, and Tangents

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  1. LESSON LESSON 11.4 PART I ANGLE MEASURES OBJECTIVE: To find the measures of angles formed by chords, secants, and tangents.

  2. REVIEW Chord: segment whose endpoints lie on a circle Secant: line that intersects the circle in two points Tangent: line that lies in the plane of a circle and intersects the circle in exactly one point

  3. Theorem 11-11: (1) The measure of an angle formed by two lines that intersect a circle is INSIDE 1/2 THE SUM OF MEASURES OF THE INTERCEPTED ARCS. FORMULA: y x 1 m1= 1/2(x + y)

  4. Theorem 11-11: (1) The measure of an angle formed by two lines that intersect a circle is OUTSIDE 1/2 THE DIFFERENCE OF MEASURES OF THE INTERCEPTED ARCS. FORMULA: m1 = 1/2(x - y) 1 y x

  5. 1 y x 1 y x 1 y x Case I Case II Case III 1 secant 1 tangent 2 secants 2 tangents

  6. EXAMPLES 1. 90º x 46º x = 1/2(46 + 90) x = 68º

  7. 2. 95º z 20º 20 = 1/2(95 - z) 40 = 95 - z -55 = -z 55º = z

  8. PRACTICE w 3. 110º 70º 70 = 1/2(w - 110) 140 = w – 110 250º = w

  9. 4. y 110º 30º y = 1/2(110 - 30) y = 40º

  10. 5. 268º 92º x x = 1/2(268 - 92) x = 88º

  11. 6. x 94º 112º 94 = 1/2(x + 112) 94 = 1/2x + 56 38 = 1/2x 76º = x

  12. ASSIGNMENT: Page 611 #1-6, 17-19, 27, 38, 41-42

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