Chords and Arcs in Circles

This video tutorial covers various theorems related to chords and circles in geometry. It begins with an introduction to congruent chords and arcs, followed by an explanation of congruent circles and their properties. The perpendicular chord bisector theorem and its converse are discussed, highlighting their implications in circle geometry. Finally, the equidistant chords theorem is explained, demonstrating how chords equidistant from the center of a circle are congruent.

What does the congruent corresponding chord theorem state about arcs and chords in the same circle?

• Two chords are different if their corresponding arcs are congruent.

• Two arcs are different if their corresponding chords are congruent.

• Two chords are congruent if their corresponding arcs are different.

• Two arcs are congruent if their corresponding chords are congruent.

In the congruent corresponding chord theorem, what must be true for two chords to be congruent in congruent circles?

• The arcs must be congruent.

• The arcs must be different.

• The circles must have different radii.

• The circles must be of different sizes.

What does the perpendicular chord bisector theorem state about a diameter and a chord?

• A diameter bisects a chord if it is shorter than it.

• A diameter bisects a chord if it is parallel to it.

• A diameter bisects a chord if it is perpendicular to it.

• A diameter bisects a chord if it is longer than it.

According to the converse of the perpendicular chord bisector theorem, what is true if one chord is a perpendicular bisector of another?

• The first chord is a diameter.

• The first chord is a tangent.

• The first chord is a radius.

• The first chord is a secant.

What does the equidistant chords theorem state about two chords in the same circle?

• They are congruent if they are equidistant from the center.

• They are different if they are equidistant from the center.

• They are different if they are different distances from the center.

• They are congruent if they are different distances from the center.

In the example problem, what is the length of the radius of Circle C?

• 14 units

• 10 units

• 8 units

• 12 units