chord, secant, tangent lengths

Front

What is a chord in a circle?

Back

A chord is a line segment whose endpoints lie on the circle.

Front

Define a secant line.

Back

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

Front

What is a tangent line?

Back

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

Front

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

Back

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

Front

What is the relationship between the lengths of secants that intersect outside a circle?

Back

If two secants intersect outside a circle, the product of the lengths of one secant segment and its external segment equals the product of the lengths of the other secant segment and its external segment.

Front

State the tangent-secant theorem.

Back

The square of the length of the tangent segment is equal to the product of the lengths of the secant segment and its external segment.

Front

If a secant intersects a circle, how do you find the length of the segment inside the circle?

Back

Use the formula: length = r^2 - d^2, where r is the radius and d is the distance from the center to the secant.

Front

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

Back

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.

Front

How do you calculate the angle formed by two chords that intersect inside a circle?

Back

The angle is equal to half the sum of the measures of the arcs intercepted by the angle.

Front

What is the formula for the area of a sector of a circle?

Back

Area = (θ/360) * πr^2, where θ is the angle in degrees and r is the radius.