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Warm up

Warm up. Day 25 – Inscribed Angles & Inscribed Quadrilaterals. Analytic geometry. Inscribed Angles and Intercepted Arcs. An _______________ is made by ___________ that SHARE an endpoint on the __________ of a circle. Where they meet is a called a _________.

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Warm up

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  1. Warm up

  2. Day 25 – Inscribed Angles & Inscribed Quadrilaterals Analytic geometry

  3. Inscribed Angles and Intercepted Arcs An _______________ is made by ___________ that SHARE an endpoint on the __________ of a circle. Where they meet is a called a _________. The arc that is between the other endpoints of the chord is called the _______________. INSCRIBED ANGLE TWO CHORDS PERIMETER VERTEX INTERCEPTED ARC

  4. Inscribed Angles and Intercepted Arcs B INSCRIBED INTERCEPTED In the diagram at the right, chords AB and BC meet at vertex __ to form ___________ ∠ABC and _____________ AC.

  5. Practice!

  6. Where are the Chords? Radius: center to a point on the circumference Tangent line: touches circle at ONE point Diameter: largest chord

  7. Where are the Vertices?

  8. Intercepted Arcs

  9. Measures of Inscribed Angles & Intercepted Arcs The measure of an inscribed angle is _____ the measure of its intercepted arcs. HALF

  10. Measures of Inscribed Angles & Intercepted Arcs 80 40 Sample: In the diagram at the right,

  11. Case I:Central Angle: Vertex is ATthe center A  P B

  12. Case II:Inscribed Angle: Vertex is ON circle  ANGLE ARC ARC  ANGLE

  13. Find the measure of DOG and DIG D 72˚ G If two inscribed angles intercept the same arc, then they are congruent. O I

  14. If all the vertices of a polygon touch the edge of the circle, the polygon is INSCRIBED and the circle is CIRCUMSCRIBED.

  15. a quadrilateral inscribed in a circle: opposite angles are supplementary. B A D C

  16. If a right triangle is inscribed in a circle then the hypotenuse is the diameter of the circle. diameter

  17. Silent, Independent Pratice Find the value of x on #4-6.

  18. Example #7

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