chord, secant, tangent lengths

Front

What is a chord in a circle?

Back

A chord is a line segment with both endpoints 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 calculate the length of a chord given the radius and the angle subtended at the center?

Back

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

Front

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

Back

A tangent is perpendicular to the radius at the point of contact.

Front

State the secant-tangent theorem.

Back

If a tangent and a secant intersect at a point outside the circle, then 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.

Front

If a secant intersects a circle, how can you find the lengths of the segments?

Back

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

Front

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

Back

Length of tangent = √(d² - r²), where d is the distance from the point to the center of the circle and r is the radius.

Front

How do you find the length of a secant segment?

Back

The length of a secant segment can be found using the secant-tangent theorem or by using the lengths of the segments created by the intersection with the circle.

Front

What is the significance of the angle subtended by a chord at the center of the circle?

Back

The angle subtended by a chord at the center of the circle helps in determining the length of the chord and the area of the sector.