Segment Lengths in Circles 2024

Front

What is the formula for finding the length of a segment when two chords intersect inside a circle?

Back

If two chords intersect inside a circle, the products of the lengths of the segments of each chord are equal. If the chords are divided into segments of lengths a, b, c, and d, then: a * b = c * d.

Tags

CCSS.HSG.C.A.2

Front

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

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 and its vertical angle.

Tags

CCSS.HSG.C.A.2

Front

How do you find the length of a segment of a chord given the radius and the distance from the center to the chord?

Back

Use the formula: length = 2 * √(r² - d²), where r is the radius and d is the distance from the center to the chord.

Tags

CCSS.HSG.C.A.2

Front

What is the definition of a secant line in relation to a circle?

Back

A secant line is a line that intersects a circle at two points.

Front

What is the definition of a tangent line in relation to a circle?

Back

A tangent line is a line that touches a circle at exactly one point.

Front

What is the formula for the length of a tangent segment drawn from a point outside the circle?

Back

If a tangent segment is drawn from a point outside the circle to the point of tangency, the length of the tangent segment is equal to the square root of the difference between the square of the distance from the point to the center and the square of the radius: length = √(d² - r²).

Tags

CCSS.HSG.C.A.2

Front

What is the relationship between the lengths of the segments of a secant line that intersects a circle?

Back

If a secant segment is divided into two parts, the product of the lengths of the entire secant segment and the external segment equals the square of the length of the tangent segment drawn from the same external point.

Tags

CCSS.HSG.C.A.2

Front

What is the definition of an arc in a circle?

Back

An arc is a portion of the circumference of a circle.

Tags

CCSS.HSG.C.B.5

Front

What is the difference between a minor arc and a major arc?

Back

A minor arc is an arc that is less than 180 degrees, while a major arc is an arc that is greater than 180 degrees.

Tags

CCSS.HSG.C.B.5

Front

How do you calculate the length of an arc?

Back

The length of an arc can be calculated using the formula: length = (θ/360) * 2πr, where θ is the central angle in degrees and r is the radius.

Tags

CCSS.HSG.C.B.5