Proofs Using Chords and Arcs

In a circle or in congruent circles, two minor arcs are congruent if and only if their corresponding ___________ are congruent.

• central angle

• inscribed angle

• intercepted arc

• congruent arc

In a circle or in congruent circles, two minor arcs are congruent if and only if their corresponding _________ are congruent

• chords

• arc

• diameter

• radius

In a circle, a diameter bisects a chord and an arc with the same endpoints if and only if it is __________ to the chord.

• parallel

• congruent

• perpendicular

• bisect

If a quadrilateral is inscribed in a circle, then its opposite angles are ___________.

• complementary

• supplementary

• congruent

• bisect

What theorem that given an angle with its vertex on a circle, formed by a secant ray and a tangent ray, the measure of the angle is half the measure of the intercepted arc.

• The Tangent-Secant Theorem

• Chord - Arc Congruence Theorem

• Distance - Chord theorem

• The Intersecting Secants - Exterior Theorem

If two chords intersect within a circle, then the measure of the angle formed is equal to half the ______ of the measures of the intercepted arcs.

• measures

• sum

• twice

• half

If a tangent and a secant, two secants, or two tangents intersect in a point in the exterior of a circle, then the measure of the angle formed is equal to one-half the ____________ of the measures of the intersected arcs.

• difference

• sum

• twice

• half

The measure of arc HJ = 110 degree and arc LJ = 150 degree, what is the measure of angle K?

In circle O, the measure of arc AB = 120 and measure of arc BC = 150. Find the measure of angle 2.

Quadrilateral LOVE is inscribed in the circle as shown. If the measure of angle V = 140 degree, what is the measure of arc ELO?

• 140⁰

• 80⁰

• 280⁰

• 40⁰