Download 10.1 Inscribed and circumscribed triangles and quadrilaterals

Key Terms
Inscribed Polygon
Inscribed right Triangle-Diameter Theorem
Inscribed Right Triangle-Diameter Converse Theorem
Circumscribed Polygon
Inscribed Quadrilateral-Opposite Angles Theorem
http://www.youtube.com/watch?v=bbxO4HdCW5A
An inscribed polygon is a polygon drawn inside a circle such that each
vertex of the polygon touches the circle.
A circumscribed polygon is a polygon drawn outside a circle such that
each side of the polygon is tangent to a circle.
pg 724 versus pg 728
You just completed the outline for a proof! 
Inscribed Right Triangle-Diameter Theorem- “If a triangle is inscribed
In a circle such that one side of the triangle is a diameter of the circle, then
The triangle is a right triangle.”
pg 725-726
The Inscribed Right Triangle-Diameter Converse Theorem- “If a right
triangle is inscribed in a circle, then the hypotenuse is a diameter of
the circle.
Notice now you are given a right triangle, hence a right angle.
By in Inscribed Angle Theorem you then know the arc opposite is
twice the measure, hence 180˚.
By definition, 180˚is a semicircle hence, the hypotenuse is a diameter.
pg 727
The Inscribed Quadrilateral-Opposite Angles theorem- “If a
quadrilateral is inscribed in a circle, then the opposite angles are
supplementary.”
A circle measures 360˚, so arc QUA  arc QDA  360
We also know the measures of the associated angles are ½
So QUA  QDA  180
pg 730
The point at which you place your compass to drawn the circle is called
the in-center and is equidistant to the sides of the polygon.
Notice the distance to the side is the radius of the circle and also
tangent.
To extend this idea to other shapes we
do the exact same thing, find the angle
bisectors, find the in-center, use the
in-center as the center of the circle to
be inscribed.
pg 731