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Inscribed Angles Tangents

Inscribed Angles Tangents. Notes 27 – Sections 10.4 & 10.5. Essential Learnings. Students will understand and be able to find measures of inscribed angles and intercepted arcs. Vocabulary. Inscribed angle – an angle with the vertex on a circle and sides are chords in a circle.

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Inscribed Angles Tangents

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  1. Inscribed AnglesTangents Notes 27 – Sections 10.4 & 10.5

  2. Essential Learnings • Students will understand and be able to find measures of inscribed angles and intercepted arcs.

  3. Vocabulary • Inscribed angle – an angle with the vertex on a circle and sides are chords in a circle. • Intercepted arc – an arc with endpoints on the sides of an inscribed angle and lies in the interior of the inscribed angle. Intercepted arc Inscribed angle

  4. Inscribed Angle Theorem • If an angle is inscribed in a circle, then the measure of the angle equals one half the measure of its intercepted arc.

  5. Example 1 • Find each measure.

  6. Theorem 10.7 • If two inscribed angles of a circle intercept the same arc or congruent arcs, then the angles are congruent.

  7. Example 2 • Find the measure of ∠R.

  8. Theorem 10.8 • An inscribed angle of a triangle intercepts a diameter or semicircle if and only if the angle is a right angle.

  9. Example 3 • Find the measure of ∠B.

  10. Theorem 10.9 • If a quadrilateral is inscribed in a circle, then its opposite angles are supplementary.

  11. Example 4 • Find the measures of angles A and D.

  12. Tangents Tangent – a line in the same plane as a circle that intersects the circle in exactlyone point called the point of tangency.

  13. Common Tangent Common tangent – a line, ray, or segment that is tangent to two circles in the same plane.

  14. Tangency Theorem In a plane, a line is tangent to a circle if and only if it is perpendicular to a radius drawn to the point of tangency.

  15. Example 5 Determine whether XY is tangent to the circle.

  16. Tangent Segments Conjecture If two segments from the same exterior point are tangent to a circle, then they are congruent.

  17. Example 6 Find x. Assume that segments that appear to be tangent are tangent. Round to the nearest tenth.

  18. Circumscribed Polygons A polygon is circumscribed about a circle if every side of the polygon is tangent to the circle.

  19. Example 7 Find the value of x. Then find the perimeter.

  20. Assignments p.713: 11 – 20, 23 – 30, 36 p. 722: 13 – 22, 24 – 27, 30 Unit Study Guide 9

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