Intersecting Chords, Tangents, and Secants

Front

What is the secant property of a circle?

Back

The secant property states that if two secants intersect outside a circle, the product of the lengths of one secant's segments equals the product of the lengths of the other secant's segments.

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 relationship between intersecting chords in a circle?

Back

When two chords intersect inside a circle, the products of the lengths of the segments of each chord are equal: (Segment 1) * (Segment 2) = (Segment 3) * (Segment 4).

Front

How do you calculate the angle formed by two intersecting chords?

Back

The measure of the angle formed by two intersecting chords is equal to half the sum of the measures of the arcs intercepted by the angle.

Front

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

Back

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

Front

What is a tangent to a circle?

Back

A tangent is a line that touches the circle at exactly one point and is perpendicular to the radius at that point.

Front

What is the relationship between a tangent and a secant that intersect at a point outside the circle?

Back

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

Front

If a secant and a tangent intersect at a point outside the circle, how do you express this relationship mathematically?

Back

If T is the length of the tangent and S is the length of the secant, then T² = S * (S - External Segment).

Front

What is the measure of an angle formed by two tangents drawn from a point outside the circle?

Back

The measure of the angle formed by two tangents from a point outside the circle is equal to half the difference of the measures of the intercepted arcs.

Front

How do you find the length of a secant segment?

Back

To find the length of a secant segment, use the secant property: (External Segment) * (Total Length) = (Other External Segment) * (Other Total Length).