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Other Angle Relationships in Circles

Other Angle Relationships in Circles. In this lesson, you will use angles formed by lines that intersect a circle to solve problems. We already know how to find the measures of several angles and their intercepted arcs. Recall,

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Other Angle Relationships in Circles

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  1. Other Angle Relationships in Circles In this lesson, you will use angles formed by lines that intersect a circle to solve problems Geometry: Circles

  2. We already know how to find the measures of several angles and their intercepted arcs. Recall, The measure of acentral angle equals ____________________________________. The following theorems will help to determine the measures of angles formed by lines which intersect on,inside or outside a circle. the measure of its intercepted arc. The measure of an inscribed angle equals ____________________________________. one-half the measure of its intercepted arc. Geometry: Circles

  3. Lines Intersecting INSIDE,OUTSIDE, or ON a Circle If two lines intersect a circle, there are three places where the lines can intersect. The following theorems will help to determine the measures of angles formed by lines which intersect inside or outside a circle. Geometry: Circles

  4. Measures of Angles Formed by Lines Intersecting ON a Circle = ½ the measure of the intercepted arc. ½ the measure of the intercepted arc Measure of angle 1 = _____ Measure of angle 2 = _____ Geometry: Circles

  5. Measures of Angles Formed by Chords Intersecting INSIDE a Circle = ½ the SUM of the Intercepted Arcs Measure of angle 1 = _____ Measure of angle 2 = ______ one-half the sum of the measures of the arcs intercepted by the angle and its vertical angle. Geometry: Circles

  6. Measures of Angles Formed by Secants and/or Tangents Intersecting OUTSIDE a Circle = ½ the DIFFERENCE of the Intercepted Arcs one-half the difference of the measures of the intercepted arcs. Geometry: Circles

  7. Measures of Angles Formed by Secants and/or Tangents Intersecting OUTSIDE a Circle Geometry: Circles

  8. Measures of Angles Formed by Lines Intersecting ON a Circle = ½ the measure of the intercepted arc. 260 m < 1 = ½ intercepted arc m < 1 = ½ (150) m <1 = _____ 75 130 = ½ intercepted arc 260 = intercepted arc Geometry: Circles

  9. ½ (174 + 106) = X ½ (280) = X 140 = X 140 Measures of Angles Formed by Chords Intersecting INSIDE a Circle = ½ the SUM of the Intercepted Arcs Geometry: Circles

  10. Measures of Angles Formed by Secants and/or Tangents Intersecting OUTSIDE a Circle = ½ the DIFFERENCE of the Intercepted Arcs 56 88 360-92= 268  ½ (200 – x) = 72 ½ (268 - 92) = x 200 – x = 144 ½ (176) = x – x = -56 Geometry: Circles

  11. In summary: The measure of an angle formed equals ½ the difference of the measures of the arcs intercepted by the angle and its vertical angle. The measure of an angle formed equals ½ its intercepted arc. The measure of an angle formed equals ½ the sum of the measures of the arcs intercepted by the angle and its vertical angle. Geometry: Circles

  12. Final Checks for Understanding Geometry: Circles

  13. Homework Assignment Angle Relationships in Triangles WS Geometry: Circles

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