Chords, Secants, and Tangents Segment Theorems

What is the Chord Theorem?

• The Chord Theorem is only applicable to equilateral triangles inscribed in a circle.

• In a circle, the product of the segments of one chord is equal to the product of the segments of the other chord.

• The Chord Theorem is a concept in music theory related to harmonics.

• The Chord Theorem states that the sum of the segments of one chord is equal to the sum of the segments of the other chord.

Tags

CCSS.HSG.C.A.2

State the Secant Theorem.

• In a circle, if a secant and a tangent intersect on the circle, then the product of the whole secant segment with its external segment is equal to the square of the tangent segment.

• The Secant Theorem applies only to right-angled triangles within a circle.

• In a circle, if a secant and a tangent intersect on the circle, then the sum of the whole secant segment with its external segment is equal to the square of the tangent segment.

• The Secant Theorem states that in a circle, if a secant and a tangent intersect on the circle, then the product of the whole secant segment with its internal segment is equal to the square of the tangent segment.

Tags

CCSS.HSG.C.A.2

Explain the Tangent Theorem.

• A line is tangent to a circle if it intersects the circle at three points.

• A line is tangent to a circle if it intersects the circle at no points.

• A line is tangent to a circle if it intersects the circle at two points.

• A line is tangent to a circle if it intersects the circle at exactly one point.

What does the Intersecting Chords Theorem state?

• Sum of segments of one chord = Sum of segments of the other chord

• Difference of segments of one chord = Difference of segments of the other chord

• Ratio of segments of one chord = Ratio of segments of the other chord

• Product of segments of one chord = Product of segments of the other chord

Tags

CCSS.HSG.C.A.2

Define the Tangent-Secant Theorem.

• The tangent segment squared is equal to the product of the secant segment and its external segment

• The length of the secant segment multiplied by its external segment is equal to the square of the tangent segment.

• The secant segment is equal to the tangent segment divided by its external segment

• The sum of the secant segment and its external segment is equal to the tangent segment

Tags

CCSS.HSG.C.A.2

In a circle, if a chord is divided into two segments by a point, what is the relationship between the products of the segments?

• The products of the segments are inversely proportional

• The products of the segments are equal.

• The products of the segments are not related

• The products of the segments are always different

Tags

CCSS.HSG.C.A.2

If two secants intersect inside a circle, what is the relationship between the products of their segments?

• Equal

• Sum

• Proportional

• Opposite

Tags

CCSS.HSG.C.A.2

What is the relationship between the angle formed by a tangent and a chord intersecting on the circle?

• The angle is always 90 degrees.

• Equal to the angle subtended by the same chord in the alternate segment.

• The angle is always greater than 180 degrees.

• The angle is always equal to the angle formed by the tangent and the radius.

Tags

CCSS.HSG.C.A.2

How can you find the length of a tangent segment from a point outside the circle?

• Divide the circumference of the circle by the distance from the point to the center

• Multiply the radius of the circle by the distance from the point to the center

• Add the radius of the circle to the distance from the point to the center

• Calculate the square root of the difference between the square of the radius of the circle and the square of the line from the point to the center.

Tags

CCSS.HSG.C.A.2

If a secant and a tangent intersect outside a circle, what is the relationship between the segments created?

• Product of whole secant segment * External segment = Tangent segment^2

• External segment * Tangent segment = Whole secant segment^2

• Sum of whole secant segment * External segment = Tangent segment^2

• External segment + Tangent segment = Whole secant segment

Tags

CCSS.HSG.C.A.2