Circle Tangents

Front

What is a tangent to a circle?

Back

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

Front

What is the point of tangency?

Back

The point of tangency is the point where the tangent line touches the circle.

Front

How is a tangent line related to the radius at the point of tangency?

Back

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

Front

If a line segment is tangent to a circle, what can be said about its distance from the center of the circle?

Back

The distance from the center of the circle to the tangent line is equal to the radius of the circle.

Front

What is the relationship between two tangent segments drawn from a common external point?

Back

The two tangent segments are congruent.

Front

How do you determine if a line segment is tangent to a circle?

Back

A line segment is tangent to a circle if it meets the circle at exactly one point and is perpendicular to the radius at that point.

Front

What is the formula for 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 significance of the tangent-secant theorem?

Back

The tangent-secant theorem states that if a tangent and a secant are drawn from a point outside the circle, 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

What is the measure of the angle formed between a tangent and a chord through the point of tangency?

Back

The measure of the angle formed is equal to the measure of the opposite arc.

Front

What is the relationship between a tangent and a circle's center?

Back

A tangent does not intersect the interior of the circle and is always at a right angle to the radius at the point of tangency.