Intersecting Chord Theorem (Chords, Angles, Arcs)

What is the Intersecting Chord Theorem?

• The Intersecting Chord Theorem states that the sum of the lengths of two chords is equal to the diameter of the circle.

• The Intersecting Chord Theorem states that if two chords intersect each other inside a circle, the products of the lengths of the segments of each chord are equal. That is, if two chords AB and CD intersect at point E, then AE * EB = CE * ED.

• The Intersecting Chord Theorem states that the angles formed by two intersecting chords are complementary.

• The Intersecting Chord Theorem states that the lengths of two intersecting chords are always equal.

What is the first step in solving a problem involving intersecting chords?

• Identify the intersecting chords and the angles formed, then apply the Intersecting Chord Theorem or angle relationships to set up equations.

• Draw a diagram of the intersecting chords without labeling any angles.

• Calculate the lengths of the chords before identifying any angles.

• Use the Pythagorean theorem to find the lengths of the chords.

If m∠PRQ = 51°, what can you infer about the intercepted arcs?

• mArc1 + mArc2 = 90°

• mArc1 + mArc2 = 102°

• mArc1 + mArc2 = 120°

• mArc1 + mArc2 = 180°

How can you apply the Intersecting Chord Theorem to find unknown lengths?

• By using the formula AE + EB = CE + ED

• By setting up an equation based on the theorem's principle (AE * EB = CE * ED) and solving for the unknown length.

• By measuring the lengths of the chords directly

• By applying the Pythagorean theorem to the intersecting chords

What is the measure of an angle formed by two intersecting chords if the intercepted arcs measure 80º and 120º?

• 80º

• 90º

• 100º

• 110º

How do you find the measure of an angle formed by two intersecting chords?

• m∠ = (arc1 + arc2) / 2

• m∠ = arc1 - arc2

• m∠ = arc1 + arc2

• m∠ = (arc1 * arc2) / 2

What is the relationship between the angles formed by intersecting chords?

• The angles are equal to the measures of the intercepted arcs.

• The angles are equal to half the sum of the measures of the intercepted arcs.

• The angles are equal to the difference of the measures of the intercepted arcs.

• The angles are independent of the intercepted arcs.

What is the formula to calculate the measure of an angle formed by two intersecting chords?

• m∠ = (mArc1 + mArc2) / 2

• m∠ = mArc1 - mArc2

• m∠ = mArc1 + mArc2

• m∠ = (mArc1 * mArc2) / 2

What is the relationship between the angles formed by two intersecting chords and the arcs they intercept?

• The measure of each angle is equal to the sum of the measures of the arcs that the angle intercepts.

• The measure of each angle is equal to half the sum of the measures of the arcs that the angle intercepts.

• The measure of each angle is equal to the difference of the measures of the arcs that the angle intercepts.

• The measure of each angle is equal to the average of the measures of the arcs that the angle intercepts.

If two chords intersect and one angle measures 70°, what is the sum of the measures of the intercepted arcs?

• 120°

• 130°

• 140°

• 150°