Tangent Lines of Circles

Front

What is a tangent line to a circle?

Back

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

Front

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

Back

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

Front

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

Back

A line is tangent to a circle if it intersects the circle at exactly one 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 external point to the center of the circle and r is the radius.

Tags

CCSS.HSG.C.A.2

Front

If two tangent segments are drawn from a single external point to a circle, what can be said about their lengths?

Back

The two tangent segments are equal in length.

Tags

CCSS.HSG.C.A.2

Front

What is the point of tangency?

Back

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

Front

Can a line be both a secant and a tangent to a circle?

Back

No, a line cannot be both a secant and a tangent. A secant intersects the circle at two points, while a tangent intersects at only one.

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 a circle, 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 part.

Tags

CCSS.HSG.C.A.2

Front

What is the angle formed between a tangent line and a radius at the point of tangency?

Back

The angle formed between a tangent line and a radius at the point of tangency is 90 degrees.

Front

How can you find the angle between two tangent lines drawn from an external point?

Back

The angle between two tangent lines drawn from an external point can be found using the formula: angle = 180° - (angle subtended by the line segment connecting the points of tangency at the center of the circle).

Tags

CCSS.HSG.C.A.2