Tangent Lines of Circles

Front

What is a tangent line to a circle?

Back

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

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

If a tangent line is drawn to a circle, what can be said about the angles formed with a radius?

Back

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

Front

How do you find the length of a tangent segment from a point outside the circle to the point of tangency?

Back

Use the Pythagorean theorem: if the distance from the point to the center of the circle is 'd' and the radius is 'r', then the length of the tangent segment 't' is given by t = √(d² - r²).

Front

What is the formula for the length of a tangent segment from an external point to a circle?

Back

Length of tangent segment = √(distance from point to center² - radius²).

Front

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

Back

The lengths of the two tangent segments are equal.

Front

What is the significance of the point of tangency?

Back

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

Front

How can you determine if a line is tangent to a circle using the distance from the center?

Back

If the distance from the center of the circle to the line is equal to the radius, then the line is tangent to the circle.

Front

What is the relationship between the angles formed by two intersecting tangents outside a circle?

Back

The angle formed between two intersecting tangents is equal to half the difference of the measures of the intercepted arcs.

Front

What is the definition of a secant line?

Back

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