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

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

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

In the circle below, diameter QS is 14 inches long and chord RT is 10 inches long. Find VU.