NO WARMUP Copy thm 12.9, corollaries, and thm

12.10 from pgs 679 and 680

12.2/12.3: CHORDS AND

ARCS & INSCRIBED

ANGLESLEQ: WHAT ARE THE THEOREMS

INVOLVED AND CALCULATIONS WITH CHORDS AND ARCS?

THEOREM SHEETThm. 12.4:1.) Congruent central angles have congruent chords

(vice versa)

2.) Congruent chords have congruent arcs

3.) Congruent arcs have congruent central angles

NOTES: PROOF OF THM. 12.4In the circle on the right, prove if

m<CAD=m<FAE, the CD=FR. C

E

F

D

A

THEOREM SHEET

Ex. 3: Find AB.

All go hand in hand:Perp, bisect, and diameter: one makes all the others true.

Ex. 4 P and Q are points on O. The distance from O to PQ is 15 in., and PQ = 16 in. Find the radius of O.

..

More examples: Find the missing lengths.

VOCAB: INSCRIBED ANGLE-an angle whose vertex is on a circle and whose

sides are chords

<ABC and <DEF are inscribed angles in the circles shown below:

<ABC intercepts minor arc AC <DEF intercepts major arc DGF

*intercept means “forms”

THEOREM 12-9: INSCRIBED ANGLE THEOREM The measure of

an inscribed angle is equal to half of its intercepted arcs.

CAmBm

21

B

A

C

EXAMPLES

Find m<ABC Find m<ABC and m<ABD

EXAMPLES

Find m<DEF and mAEC Find m<ABC

3 INSCRIBED < COROLLARIES

If two inscribed angles

intercept the same arc, then the

angles are congruent.

An angle inscribed in a semicircle is a right angle.

If a quadrilateral is inscribed in a circle, then its opposite angles are

supplementary.

THEOREM 12-10The measure of an angle formed by a chord and a

tangent is equal to half the measure of the intercepted arc.

B

D

C C

BD

mBDCCm21

EX: FIND THE NUMBERED ANGLES.

1 2

108˚

32˚

1

161˚

12102˚

46˚

HWK: Copy thms 12.11 and 12.12