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Secant Angles

A secant is a straight line that intersects a circle or curve. A secant angle is formed by two secant lines originating from a point outside the circle. The measure of a secant angle can be calculated as half the difference between the measures of the intercepted arcs. For example, if arcs measure 100° and 20°, the secant angle is 40°. This concept also extends to solving for missing arcs using the relationship between secant angles and arcs.

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Secant Angles

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  1. Secant Angles Arcs and Secant Lines

  2. A Secant is a straight line that crosses/intercepts another shape. A Secant angle is an angle made from two secant lines.

  3. Arcs and Secant Angles • The secant angle equals half the difference between the measure of the two arcs (for A outside the circle). B D A E C

  4. Arcs and Secant Angles • The secant angle is half of Arc BC – Arc DE • Secant Angle = ½ (100 – 20) A=___ 40° ½ (80) = 40° B 100° D 20° A E C

  5. Arcs and Secant Angles A= 30° • Given the Angle: Solve for missing arc. A = ½ (BC – DE) 30 = ½ (110 – x) BC= 110° 2(30) = (110 – x) 50° DE= ___ 60 = (110 – x) B 110° D A 30° E C

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