Secant, Tangent, and Chord Lengths

Front

What is 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

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 chord given the radius and the angle subtended at the center?

Back

Use the formula: Length of chord = 2 * r * sin(θ/2), where r is the radius and θ is the angle in radians.

Tags

CCSS.HSG.C.A.2

Front

What is the relationship between the lengths of secants and tangents drawn from an external point?

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 part (Power of a Point Theorem).

Tags

CCSS.HSG.C.A.2

Front

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

Back

Use the formula: (Length of first secant) * (Length of external part) = (Length of second secant) * (Length of external part).

Tags

CCSS.HSG.C.A.2

Front

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

Back

Length of tangent = √(d^2 - r^2), where d is the distance from the point to the center of the circle and r is the radius.

Tags

CCSS.HSG.C.A.2

Front

How do you calculate the length of a secant segment?

Back

The length of a secant segment can be calculated using the coordinates of the points where it intersects the circle.

Tags

CCSS.HSG.C.A.2

Front

What is the significance of the angle formed by a tangent and a chord?

Back

The angle formed by a tangent and a chord through the point of contact is equal to the angle subtended by the chord in the opposite arc.

Tags

CCSS.HSG.C.A.2

Front

What is the relationship between the radius and the tangent at the point of contact?

Back

The radius drawn to the point of tangency is perpendicular to the tangent line.