Intersecting Chord Theorem (Chords, Angles, Arcs)

Front

What is the Intersecting Chord Theorem?

Back

The Intersecting Chord Theorem states that if two chords intersect inside a circle, the products of the lengths of the segments of each chord are equal.

Front

If two chords AB and CD intersect at point E, how can you express the relationship between the segments?

Back

If AE and EB are segments of chord AB, and CE and ED are segments of chord CD, then AE × EB = CE × ED.

Front

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

Back

The measure of the angle formed by two intersecting chords is equal to half the sum of the measures of the arcs intercepted by the angle.

Front

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

Back

To find the measure of the angle, add the measures of the two arcs intercepted by the angle and divide by 2.

Front

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

Back

m∠ = (mArc1 + mArc2) / 2.

Front

If the arcs intercepted by an angle measure 80° and 40°, what is the measure of the angle?

Back

m∠ = (80° + 40°) / 2 = 60°.

Front

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

Back

The angles formed by two intersecting chords are vertical angles and are equal to each other.

Front

How do you calculate the length of a chord in a circle?

Back

The length of a chord can be calculated using the formula: length = 2 * r * sin(θ/2), where r is the radius and θ is the central angle.

Front

What is the significance of the center of a circle in relation to chords?

Back

The center of a circle is equidistant from all points on the circle, and it helps in determining the lengths and angles related to chords.

Front

What happens to the angles when two chords intersect outside the circle?

Back

When two chords intersect outside the circle, the measure of the angle formed is equal to half the difference of the measures of the intercepted arcs.