107 Inscribed And Circumscribed PolygonsI Inscribed

10.7 Inscribed and Circumscribed Polygons

I. Inscribed and Circumscribed Polygons
A polygon is inscribed in a circle if all of its vertices lie on the circle.
A polygon is circumscribed about a circle if each of its sides is tangent to the circle.
The center of a circle circumscribed about a polygon is the circumcenter of the polygon.
The center of a circle inscribed in a polygon is the incenter of the polygon.

II. Inscribed Quadrilaterals
Thm 93: “If a quadrilateral is inscribed in a circle, then its opposite angles are supplementary.

supp.

supp.

Thm 94: “If a parallelogram is inscribed in a circle, then it must be a rectangle.”

ABCD is a parallelogram

ABCD is a rectangle

Ex#1:
If the measure of arc MAT is and , find the measures of and .

Ex#2:
ABCD is a parallelogram inscribed in a circle. If and measure of arc BC is , find the area of the circle.

CW: 10.7 p.489-490 #1-9, #11, #13-14, #18, #21-23 HW: 10.7 p.489-490 #10, #12, #15-17, #19-20, #24