Secants and Tangents in a Circle

Front

What is a tangent to a circle?

Back

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

Front

What is a secant in relation to a circle?

Back

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

Front

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

Back

The tangent is perpendicular to the radius at the point of tangency.

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 secant-tangent theorem?

Back

The secant-tangent theorem states that 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 entire secant segment and its external segment.

Front

If a tangent segment measures 10 units, what is the relationship to the secant segment that intersects it?

Back

If the tangent segment is 10 units, then the square of this length (10² = 100) equals the product of the secant segment's lengths.

Front

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

Back

The length of a secant segment can be expressed as: length = a + b, where 'a' is the external segment and 'b' is the internal segment.

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 of first secant) = (length of second secant) × (length of external part of second secant).

Front

What is the angle formed between 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 formed by two secants intersecting outside the circle?

Back

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