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6.10 – Circles and Polygons
Key Terms
No key terms for this section.
Review
 A polygon is a closed plane figure with all straight sides.
 A parallelogram is a quadrilateral with parallel opposite sides
 A rectangle is a parellelogram with all right angles and congruent opposite sides
A square is a rectangle with all congruent sides.
 Angles
 Inscribed angle – An angle formed by two chords that share an endpoint on a circle.
 It is half the measure of the intercepted arc.
 Supplementary angles – Two angles whose measures have the sum of 180°.
 Complementary angles – Two angles whose measures have the sum of 90°

Notes
Incenters and Circumcenters of Polygons 
 The ideas of incenter and circumcenter for all polygons are the same as what you have seen for triangles.



Inscribed and Circumscribed Circles 
 Circle Inscribed in a Polygon
 The circle is inside the polygon and tangent to each side of the polygon.

 Circle Circumscribed About a Polygon
 The circle is wrapped around the outside of the polygon and intersects each of the polygon’s vertices.
 Quadrilaterals inscribed in circles
 The measures of opposite angles of a quadrilateral (4 sided polygon) add up to 180° (supplementary).
 The ONLY parallelogram that can be inscribed in a circle is a rectangle.
 All squares are rectangles.

Examples
 Ex 1. In the diagram below, is circumscribed about quadrilateral ABCD. What is the value of x?
 Since opposite angles are supplementary, x + 120 = 180.
 Subtract 120 on both sides: x = 60

Important!
Practice (Apex Study 6.10)
 Try practice problems on Pgs 13, 19
 Mandatory: write and answer problems on Pg 20
 1 Quiz
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