 Copy thm 12.9, corollaries, and thm 12.10 from pgs 679 and 680.

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Presentation transcript:

 Copy thm 12.9, corollaries, and thm from pgs 679 and 680

LEQ: WHAT ARE THE THEOREMS INVOLVED AND CALCULATIONS WITH CHORDS AND ARCS?

Thm. 12.4: 1.) Congruent central angles have congruent chords (vice versa) 2.) Congruent chords have congruent arcs 3.) Congruent arcs have congruent central angles

In the circle on the right, prove if m<CAD=m<FAE, the CD=FR. C E F D A

Ex. 3: Find AB.

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

Ex. 4P 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.

- 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”

 The measure of an inscribed angle is equal to half of its intercepted arcs. B A C

Find m<ABCFind m<ABC and m<ABD

Find m<DEF and mAEC Find m<ABC

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.

The measure of an angle formed by a chord and a tangent is equal to half the measure of the intercepted arc. B D CC B D

12 108˚ 32˚ ˚ ˚ 46˚

 Copy thms and 12.12