10.3 arcs and chords if two chords are congruent, then their arcs are also congruent inscribed...
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10.3 Arcs and Chords
If two chords are congruent, then their arcs are also congruent
Inscribed quadrilaterals: the opposite angles are supplementary
If a radius or diameter is perpendicular to a chord, it bisects the chord and its arc
If two chords are equidistant from the center of the circle, the chords are congruent
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AB
C
DE
F
If FE=BC, then arc FE = arc BC
Quad. BCEF is an inscribed polygon – opposite angles are supplementary
angles B + E = 180 & angles F + C = 180
Diameter AD is perpendicular to chord EC – so chord EC and arc EC are bisected
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E
A
B
C F D
X
*You can use the pythagorean theorem to find the radiuswhen a chord is perpendicular to a segment from the center
XE = XF so chord AB = chord CD because they are equidistant from the center
You will need to draw in the radius yourself
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In the circle below, diameter QS is 14 inches long and chord RT is 10 inches long. Find VU.
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