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Homework Review

UNIT QUESTION: What special properties are found with the parts of a circle? Standard: MMC9-12.G.C.1-5,G.GMD.1-3 Today’s Question: How can I find a segment length for a piece of a chord? Standard: MMC9-12.G.C.2 GPS Geometry Day 25 ( )

How do you know when two chords are congruent? LP  PM ALP = BMP = 90 a.corresponding arcs are congruent A B C D M L P b. equidistant from the center

Flow Chart Proof

2x x x = x + 40 x = 40

In  K, K is the midpoint of RE. If TY = -3x + 56 and US = 4x, find the length of TY. Y T S K x = 8 TY = 32 U R E

A B C D IF AC is the perpendicular bisector of segment DB, then… It’s the DIAMETER!!! Arcs DC and BC are congruent!!!

IN  Q, KL  LZ. IF CK = 2X + 3 and CZ = 4x, find x. K Q C L Z x = 1.5

In  P, if PM  AT, PT = 10, and PM = 8, find AT. T A M P MT = 6 AT = 12

Your turn!  UTV   XTW. Find WX.___________ Find ___________ º

Your turn! Find the length of each chord. CE = _______ LN = _______ 30 96

Segment Lengths in Circles  Find the lengths of segments of chords  Find the lengths of segments of tangents and secants

a b c d ab = cd

9 2 6 x x = 3 Solve for x.

Find the length of DB x 3x x = 4 DB = 20 A B C D

Find the length of each chord. x = 8 AC = 13 DB = 14 x 5 x A B C D

EAB C D EA EB = EC ED

E A B C D x 7(7 + 13) 4(4 + x) = Ex: 3 Solve for x. 140 = x 124 = 4x x = 31

E A B C D x 6(6 + 8) 5(5 + x) = Ex: 4 Solve for x. 84 = x 59 = 5x x = 11.8

E A B C EA 2 = EB EC

E A B C x 24 2 =12 (12 + x) 576 = x x = 36 Ex: 5 Solve for x.

E A B C 15 5 x x2x2 =5 (5 + 15) x 2 = 100 x = 10 Ex: 6