Secants and Tangents in a Circle

Front

What is a secant in a circle?

Back

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

Front

What is a tangent in a circle?

Back

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

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

If two secants intersect outside a circle, how do you find the measure of the angle formed?

Back

The measure of the angle is half the difference of the measures of the intercepted arcs.

Front

What is the formula for the power of a point theorem?

Back

If a point P is outside a circle, then the power of P is equal to the square of the length of the tangent segment from P to the circle.

Front

How do you calculate 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 = √(d² - r²), where d is the distance from the point to the center of the circle and r is the radius.

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

Back

The products of the lengths of the segments of each secant are equal: (a)(b) = (c)(d), where a and b are the segments of one secant and c and d are the segments of the other.

Front

What is the measure of an angle formed by two secants that intersect outside a circle?

Back

The measure of the angle is half the difference of the measures of the intercepted arcs.

Front

How do you find the measure of an arc intercepted by a tangent and a secant?

Back

The measure of the arc is equal to half the measure of the angle formed by the tangent and the secant.