Tangent to a circle

Front

What is a tangent line?

Back

A tangent line is a straight line that touches a circle at exactly one point, known as the point of tangency.

Front

What angle is formed when a tangent line intersects a radius at the point of tangency?

Back

A right angle (90 degrees) is formed when a tangent line intersects a radius.

Front

If point O is the center of a circle, what can be said about the distance from O to the point of tangency?

Back

The distance from point O to the point of tangency is equal to the radius of the circle.

Front

How many tangent lines can be drawn to a circle from a single external point?

Back

Two tangent lines can be drawn from a single external point to a circle.

Front

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

Back

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

Front

If a tangent line is drawn to a circle, what can be said about the segments created by the tangent and a line drawn from the center to the point of tangency?

Back

The segments are equal in length to the radius of the circle.

Tags

CCSS.HSG.C.A.2

Front

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

Back

The length of the tangent segment can be found using the Pythagorean theorem: length = √(d^2 - r^2), where d is the distance from the external point to the center of the circle and r is the radius.

Tags

CCSS.HSG.C.A.2

Front

What is the significance of the point of tangency in relation to the circle?

Back

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

Front

Can a tangent line intersect the circle at more than one point?

Back

No, a tangent line can only intersect the circle at one point.

Front

What is the difference between a tangent and a secant line?

Back

A tangent line touches the circle at one point, while a secant line intersects the circle at two points.