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Geometry Inscribed Angles and Circles

Learn about inscribed angles, intercepted arc theorem, and properties of polygons inscribed in circles. Understand circle theorems and examples to enhance your geometry knowledge.

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Geometry Inscribed Angles and Circles

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  1. Warm up (TI) • Determine whether the arc is a minor arc, major arc or semicircle. • PLM • NL • mLN • mPLN • x L M 40° 142° 38° N K 5x° P

  2. Inscribed Angles Chapter 10 section 3

  3. What is an inscribed angle? • An inscribed angle is an angle whose vertex is on a circle and whose sides contain chords of the circle. Intercepted arc

  4. Theorem • An inscribed angle is ½ the measure of its intercepted arc. B m<BOM = 1/2mBM O M

  5. Examples • Find the following measures. P S m PSR= Q R

  6. Example W m ZWX = Z X 115° Y

  7. Example N 100° M m< NMP = P

  8. Find the m<ACB, m<ADB and m<AEB A 60° B E C D

  9. Theorem • If two inscribed angles of a circle intercept the same arc, then they are congruent!

  10. Inscribed/Circumscribed • A polygon is inscribed in a circle if all the vertices of the polygon lie on the circle. • The circle above is circumscribed about the polygon.

  11. Theorem • If a right triangle is inscribed in a circle, then the hypotenuse is a diameter of the circle. The converse is also true.

  12. Theorem • A quadrilateral can be inscribed in a circle iff the opposite angles are supplementary. O M V E

  13. 3x Example • Find the value of each variable. y x 85 80

  14. Example…you’ll love this! • Find the measure of each angle. B 19y 10y A C 40x 22x D

  15. Complete Assignment #3

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