Inscribed Polygons Inscribed Polygons

You will learn to inscribe regular polygons in circles and explorethe relationship between the length of a chord and its distancefrom the center of the circle.

1) circumscribed

2) inscribed

Inscribed Polygons Inscribed Polygons

When the table’s top is open, its circular top is said to be ____________about the square.

circumscribed

We also say that the square is ________ in the circle. inscribed

Definition of

Inscribed Polygon

A polygon is inscribed in a circle if and only if every vertex of the polygon lies on the circle.

Inscribed Polygons Inscribed Polygons

A

F

B

C

D E

Some regular polygons can be constructed by inscribing them in circles.

Inscribe a regular hexagon, labelingthe vertices, A, B, C, D, E, and F.

Construct a perpendicular segment from the center to each chord.

From our study of “regular polygons,” we know that the chords

AB, BC, CD, DE, and EF are_________congruent

From the same study, we also know that all of the perpendicular segments,called ________, are _________.apothems congruent

Make a conjecture about the relationship between the measure of the chordsand the distance from the chords to the center.

The chords are congruent because the distances from the center of the circle are congruent.

P

Inscribed Polygons Inscribed Polygons

Theorem11-6

In a circle or in congruent circles, two chords are congruentif and only if they are __________ from the center.equidistant

L

M

P

CD

B

A

AD BCiff

LP PM

Inscribed Polygons Inscribed Polygons

O

S

T

B

A

C

RIn circle O, O is the midpoint of AB.

If CR = -3x + 56 and ST = 4x,find x

OA= OB definition of midpoint

CR= ST Theorem 11-6

−3x+56= 4x substitution

56=7x

8= x