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Mathematics · Grade 10

Circles, Arcs and Angles

Learners relate central angles, arcs and inscribed angles and prove the inscribed angle theorem, including the right angle in a semicircle and the supplementary opposite angles of a cyclic quadrilateral. They use tangent and chord properties, compute arc lengths and sector areas, meet radian measure as arc length divided by radius, and write and analyze equations of circles on the coordinate plane.

  • 4 lessons
  • About 130 minutes
  • Circles check: 11 questions
  • Ways to answer: choose an answer, plot points, match pairs, type a number, true or false and write a short answer
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What learners will discover

  • Relate central angles, arcs and inscribed angles, and apply the inscribed angle theorem, the angle in a semicircle and cyclic quadrilaterals.
  • Apply properties of tangents (a tangent is perpendicular to the radius at the point of tangency; tangent segments from a point are congruent) and of chords.
  • Compute arc lengths and sector areas, explain why all circles are similar, and define radian measure as arc length divided by radius.
  • Write the equation of a circle from its center and radius and find the center and radius of a circle by completing the square.

Lessons

  1. Central and inscribed angles 7 steps5 practiceabout 32 min
  2. Tangents and chords 6 steps4 practiceabout 30 min
  3. Arc length, sector area and radians 6 steps4 practiceabout 32 min
  4. Equations of circles 6 steps4 practiceabout 30 min
  5. Circles check 11 questions at the end

Keep exploring

More 10th grade math

Guide for grown-ups