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Circle Angle Relationships Theorems Explained

Learn about angle relationships in circles with Theorems 10-12, 10-13, and 10-14. Discover how tangents, chords, secants, and arcs intersect, and master the angles formed in and outside circles.

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Circle Angle Relationships Theorems Explained

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  1. Section 10-4 Other Angle Relationships in Circles

  2. Theorem 10-12 • If a tangent and a chord intersect at a point on a circle, then the measure of each angle formed is one half the measure of its intercepted arc.

  3. A is tangent to Circle O is a chord in Circle O O T P Example:

  4. If two lines intersect a circle, there are three places where the lines can intersect.

  5. On a circle

  6. inside a circle

  7. Outside a circle

  8. Theorem 10-13 • If two chords intersect inside a circle, then the measure of each angle is one half the sum of the measures of the arcs intercepted by the angle and its vertical angle.

  9. A D 1 C B

  10. Theorem 10-14 • If a tangent and a secant, two tangents, or two secants, intersect outside a circle, then the measure of the angle formed is one half the difference of the measures of the intercepted arcs.

  11. 3 A tangent and a secant:

  12. 2 Two tangents:

  13. 1 Two secants:

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