Segment Measurements with Tangents, Secants, and Chords

Front

What is a tangent in relation to a circle?

Back

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

Front

What is a secant in relation to a circle?

Back

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

Front

What is a chord in a circle?

Back

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

Front

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

Back

The length of the tangent segment can be found using the formula: length = √(distance from point to center² - radius²).

Front

What is the relationship between the lengths of tangents drawn from an external point to a circle?

Back

The lengths of the tangents drawn from an external point to a circle are equal.

Front

If two chords intersect inside a circle, how do you find the lengths of the segments?

Back

The products of the lengths of the segments of each chord are equal: (a)(b) = (c)(d).

Front

What is the formula for the length of a chord in a circle?

Back

The length of a chord can be calculated using the formula: length = 2 * r * sin(θ/2), where r is the radius and θ is the central angle.

Front

What is the angle formed by a tangent and a chord through the point of contact?

Back

The angle formed is equal to the measure of the opposite arc.

Front

How do you calculate the angle between two secants that intersect outside a circle?

Back

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

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 product of the lengths of the segments of any secant line through the point is equal to the square of the length of the tangent segment from the point to the circle.