B ELLWORK ACT Review: (x, y) is the midpoint of a segment with endpoints (2, -3) and (8, 9). What is the sum of x and y ? Geometry Review: Find the length.

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Presentation transcript:

B ELLWORK ACT Review: (x, y) is the midpoint of a segment with endpoints (2, -3) and (8, 9). What is the sum of x and y ? Geometry Review: Find the length of the black arc in the circle below.

10.3 A RCS AND C HORDS Students will be able to identify the distance from the center to a chord, apply the radius to chord theorem, and the congruent chord = congruent arc theorem.

C HORD -A RC T HEOREM If __________, then ____________.

D ISTANCE TO A CHORD FROM CENTER : How would you measure the distance from center O to chord ?

R ADIUS -C HORD T HEOREM If a radius is perpendicular to a chord, then it bisects the chord.

C HORD D ISTANCE T HEOREMC HORD D ISTANCE T HEOREM If two chords are congruent, then they are ___________from the center (and the converse also is true!) Here: If __________, then ___________.

E XAMPLE 1 Find the distance from the center of a circle to a chord 30 m long if the radius of the circle is 17m.

E XAMPLE 2 The diameter of the circle is 26 inches. If the distance to the center of the chord is 5, how long is the chord?

E XAMPLE 3

E XAMPLE 4 Given:, DE = 24 AB = 4x + 6, FG = 10x – 6 Find: AB and the radius of.

T ICKET TO L EAVE The chord of a circle is 24 inches long. What is the radius of the circle if the distance from the center to the chord is 5 inches?

H OMEWORK Pg.574 #2, 20 – 29, 32, 37 – 39, 53 – 57 EC for a well-written solution to #30. Quiz Friday 3/13