Intersecting Chord Theorem (Chords, Angles, Arcs)

Front

What is the Intersecting Chord Theorem?

Back

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.

Tags

CCSS.HSG.C.A.2

Front

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

Back

To find the measure of an angle formed by two intersecting chords, you can use the formula: m∠ = (arc1 + arc2) / 2, where arc1 and arc2 are the measures of the arcs intercepted by the angle.

Tags

CCSS.HSG.C.A.2

Front

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

Back

The angles formed by intersecting chords are related to the arcs they intercept. Specifically, the measure of an angle formed by two intersecting chords is equal to half the sum of the measures of the arcs intercepted by the angle.

Tags

CCSS.HSG.C.A.2

Front

If two chords intersect inside a circle, how can you express the lengths of the segments?

Back

If two chords AB and CD intersect at point E, the lengths of the segments can be expressed as AE, EB, CE, and ED. According to the Intersecting Chord Theorem, AE * EB = CE * ED.

Tags

CCSS.HSG.C.A.2

Front

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

Back

The formula to calculate the measure of an angle formed by two intersecting chords is: m∠ = (mArc1 + mArc2) / 2.

Tags

CCSS.HSG.C.A.2

Front

How do you determine the value of x in an intersecting chords problem?

Back

To determine the value of x in an intersecting chords problem, set up an equation based on the Intersecting Chord Theorem or the angle relationships, and solve for x.

Tags

CCSS.HSG.C.A.2

Front

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

Back

The measure of the angle is (80º + 120º) / 2 = 100º.

Tags

CCSS.HSG.C.A.2

Front

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

Back

If m∠PRQ = 51°, then the measure of the intercepted arcs can be calculated using the formula: mArc1 + mArc2 = 2 * m∠PRQ, which gives mArc1 + mArc2 = 102°.

Tags

CCSS.HSG.C.A.2

Front

What is the significance of the Intersecting Chord Theorem in solving geometry problems?

Back

The Intersecting Chord Theorem is significant because it provides a method to relate the lengths of segments of intersecting chords and the measures of angles formed, which is essential for solving various geometry problems involving circles.

Tags

CCSS.HSG.C.A.2

Front

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

Back

You can apply the Intersecting Chord Theorem by setting up an equation based on the theorem's principle (AE * EB = CE * ED) and solving for the unknown length.

Tags

CCSS.HSG.C.A.2