1. Warm Up Determine the measures of the indicated angles. 1.2. Now put it all together to solve for the missing angle.

2. Unit 6 – Day 3 Inscribed and Circumscribed

3. Today’s Objectives Students will use properties of Central angles and Tangent lines to solve for missing parts Students will define inscribed and circumscribed polygons Students will explore properties of Inscribed and Circumscribed Triangles and Quadrilaterals

4. Using Properties of Central Angles and Tangent Lines Things to remember: Radius and Tangent form a _______ angle. We can use ___________________ Theorem for Right Triangles: Use the properties of Tangent Lines, Central Angles, and Inscribed Angles to solve for the missing parts

5. Defining Inscribed and Circumscribed Polygons Guided Notes Definitions Inscribed: A polygon is inscribed in a circle if all of the vertices lie on the circle. Circumscribed: A polygon is circumscribed about a circle if each side is tangent to the circle.

6. Exploration Use the properties of inscribed angles to find the missing angles Given: m ∠ ADC=60˚, mBC=40˚and mCD=110˚, find m ∠ ABC. Then find m ∠ BCD and m ∠ DAB m ∠ ABC =_________ m ∠ BCD =_________ m ∠ DAB =_________ What do you notice about opposite angles in the quadrilateral? – Supplementary About the sum of all angles? – 360º Therefore, opposite angles of an inscribed quadrilateral are supplementary!

7. Inscribed or Circumscribed? Describe the relationship between the polygon and the circle using “inscribed” and “circumscribed”?

8. Inscribed or Circumscribed? Describe the relationship between the polygon and the circle using “inscribed” and “circumscribed”?

9. Inscribed or Circumscribed? Describe the relationship between the polygon and the circle using “inscribed” and “circumscribed”?

10. Relationships Triangle Inscribed in a Circle http://www.geogebratube.org/student/m34411 7 Triangle Circumscribed about a Circle http://www.geogebratube.org/student/m34410 5

11. Centers The center of inscribed circle of a triangle is the intersection of the angle bisectors. The center of a circumscribed circle of a triangle is the intersection of the perpendicular bisectors.

12. Homework