Tangent Lines to a Circle

Front

What is a tangent line to a circle?

Back

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

Front

What is the point of tangency?

Back

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

Front

How many tangents can be drawn from a point outside a circle?

Back

Two tangents can be drawn from a point outside a circle.

Front

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

Back

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

Front

What is the formula for finding 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: \( L = \sqrt{d^2 - r^2} \), where \( d \) is the distance from the point to the center of the circle and \( r \) is the radius.

Front

What are common tangents?

Back

Common tangents are lines that are tangent to two circles at the same time.

Front

How many types of common tangents are there?

Back

There are two types of common tangents: external tangents and internal tangents.

Front

What is an external tangent?

Back

An external tangent is a tangent line that does not intersect the line segment connecting the centers of the two circles.

Front

What is an internal tangent?

Back

An internal tangent is a tangent line that intersects the line segment connecting the centers of the two circles.

Front

How do you determine the number of common tangents between two circles?

Back

The number of common tangents depends on the relative positions of the circles: 0, 1, 2, or 3 common tangents can exist.