Tangent lines with 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 tangent line and a radius at the point of tangency?

Back

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

Front

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

Back

The length of the tangent segment can be found using 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 circumference of a circle?

Back

The circumference C of a circle is given by the formula C = 2πr, where r is the radius.

Front

What is the area of a circle?

Back

The area A of a circle is given by the formula A = πr², where r is the radius.

Front

If a tangent line intersects a circle, what can be said about the angles formed?

Back

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

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, and it is crucial for determining the relationship between the tangent and the radius.

Front

How can you prove that a line is a tangent to a circle?

Back

To prove a line is a tangent, show that it is perpendicular to the radius at the point of contact.

Front

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

Back

The lengths of the two tangent segments drawn from a single external point to a circle are equal.

Front

What is 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, then 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.