A chord is defined as a line segment whose endpoints lie on the circle's circumference. The other options describe parts of a circle that do not meet this definition.

An arc is a portion of a circle's circumference that lies between two distinct points. It is different from a chord, which is the straight line connecting those two points.

A semicircular arc represents half of a full circle and measures 180 degrees. Therefore, the central angle intercepting that semicircle also measures 180 degrees.

Equal chords in a circle cut off arcs of equal measure. This is a key property in circle geometry that links chord lengths with their intercepted arcs.

The diameter is the longest chord in a circle because it passes through the center and spans the greatest distance across the circle. Other chords, not passing through the center, are necessarily shorter.

The Inscribed Angle Theorem states that an inscribed angle is half the measure of its intercepted arc. Therefore, a 30-degree inscribed angle intercepts an arc of 60 degrees.

When two chords in a circle are parallel, the arcs between them on the same side of the chords are congruent. This is due to the symmetry present in the circle.

By definition, the measure of a central angle is equal to the measure of its intercepted arc. This direct correlation is one of the basic properties in circle geometry.

The Inscribed Angle Theorem states that an inscribed angle is half the measure of its intercepted arc. This theorem is essential in solving many circle geometry problems involving chords and arcs.

The Inscribed Angle Theorem tells us that an inscribed angle is half the measure of the central angle that intercepts the same arc. This relationship is a fundamental aspect of circle geometry.

The chord length is given by the formula: chord = 2r sin(angle/2). Substituting r = 10 cm and angle = 60° yields chord = 20 sin(30°) = 20 × 0.5 = 10 cm.

The Angle Between Tangent and Chord Theorem states that the angle between a tangent and a chord is equal to the inscribed angle in the alternate segment. This theorem is useful in relating tangents to circle arcs.

The Intersecting Chords Theorem states that when two chords intersect inside a circle, the product of the segments of one chord equals the product of the segments of the other chord. This property is frequently used in solving problems involving intersecting chords.

According to the Inscribed Angle Theorem, the intercepted arc is twice the measure of the inscribed angle. Therefore, an inscribed angle of 45 degrees intercepts an arc of 90 degrees.

The perpendicular bisector of any chord in a circle always passes through the circle's center. This property is often used to determine the center of a circle.

For intersecting chords, the measure of the angle is half the sum of its intercepted arcs. Setting up the equation 80 = ½(120 + x) and solving for x gives 40 degrees.

Using the chord length formula, chord = 2r sin(angle/2), we substitute 16 = 20 sin(angle/2) to get sin(angle/2) = 0.8. Thus, angle/2 ≈ 53.13° and the full central angle is approximately 106.3°.

Opposite angles in a cyclic quadrilateral are supplementary, meaning their measures add up to 180°. Therefore, the angle opposite an 80° angle measures 100°.

The angle formed by two secants intersecting outside a circle equals half the difference of the measures of the intercepted arcs. Here, half of (110° - 70°) is 20°.

According to the Inscribed Angle Theorem, an inscribed angle is half the measure of its intercepted arc. Therefore, an arc of 140° will subtend an inscribed angle of 70°.