http://www.ck12.org Chapter 9. Circles
9.6 Inscribed Quadrilaterals in Circles
Here you’ll learn properties of inscribed quadrilaterals in circles and how to apply them.
What if you were given a circle with a quadrilateral inscribed in it? How could you use information about the
arcs formed by the quadrilateral and/or the quadrilateral’s angle measures to find the measure of the unknown
quadrilateral angles? After completing this Concept, you’ll be able to apply the Inscribed Quadrilateral Theorem to
solve problems like this one.
Watch This
MEDIA
Click image to the left for more content.CK-12 Foundation: Chapter9InscribedQuadrilateralsinCirclesA
MEDIA
Click image to the left for more content.Brightstorm:Cyclic Quadrilaterals and Parallel Lines inCircles
Guidance
Aninscribed polygonis a polygon where every vertex is on a circle. Note, that not every quadrilateral or polygon
can be inscribed in a circle. Inscribed quadrilaterals are also calledcyclic quadrilaterals. For these types of
quadrilaterals, they must have one special property. We will investigate it here.
Investigation: Inscribing Quadrilaterals
Tools Needed: pencil, paper, compass, ruler, colored pencils, scissors
- Draw a circle. Mark the center pointA.
- Place four points on the circle. Connect them to form a quadrilateral. Color the 4 angles of the quadrilateral 4
different colors. - Cut out the quadrilateral. Then cut the quadrilateral into two triangles, by cutting on a diagonal.
- Line up^6 Band^6 Dso that they are adjacent angles. What do you notice? What does this show?