Inscribed Angles & Inscribed Quadrilaterals

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Presentation transcript:

Inscribed Angles & Inscribed Quadrilaterals Math II Unit 5: Circles

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

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

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

Where are the Vertices?

Intercepted Arcs

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

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

Case I: Central Angle: Vertex is AT the center A  P B

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

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

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

a quadrilateral inscribed in a circle: opposite angles are supplementary.

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

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

Example #7