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 of chord = 2 * √(r² - d²), 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 two tangent segments drawn from a point outside the circle?

Back

The lengths of the two tangent segments are equal.

Front

If two secants intersect outside a circle, how do you find the length of the segments?

Back

Use the formula: (external segment 1) * (total length of secant 1) = (external segment 2) * (total length of secant 2).

Front

What is the power of a point theorem?

Back

The power of a point theorem states that for a point outside a circle, the square of the length of the tangent segment from the point to the circle is equal to the product of the lengths of the segments of any secant line drawn from that point.

Front

How do you calculate the length of a tangent segment from a point outside the circle?

Back

Use the formula: length of tangent = √(distance from point to center² - radius²).

Front

What is the formula for the length of a secant segment?

Back

The length of a secant segment can be found using the formula: length = √(external segment) * (total length of secant).

Front

If a circle has a radius of 10 and a chord is 12 units from the center, what is the length of the chord?

Back

Length of chord = 2 * √(10² - 12²) = 2 * √(100 - 144) = 2 * √(-44) (not possible, check values).