Inscribed Angles Inscribed Quadrilaterals MATH II UNIT 5

Inscribed Angles & Inscribed Quadrilaterals MATH II UNIT 5: CIRCLES

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

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

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 HALF the �The measure of an inscribed angle is _____ measure of its intercepted arcs.

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 AR C ARC E GL AN

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

If a right triangle is inscribed in a circle then the hypotenuse is the diameter of the circle. am di r e et

Silent, Independent Pratice FIND THE VALUE OF X ON #4 -6.

Example #7