Tangent Lines and Chords of a Circle Exit Ticket

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 a chord in a circle?

Back

A chord is a line segment whose endpoints both lie on the circle.

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, where the length of the tangent segment is the square root of the difference between the square of the distance from the point to the center of the circle and the square of the radius.

Front

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

Back

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

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 of the circle, then the line is tangent to the circle.

Front

What is the formula for the length of a chord in a circle?

Back

The length of a chord can be calculated using the formula: L = 2 * r * sin(θ/2), where r is the radius and θ is the central angle in radians.

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 angles and distances related to the circle.

Front

How do you find the perimeter of a shape involving tangents and chords?

Back

To find the perimeter, sum the lengths of all the tangent segments and chord segments that make up the shape.

Front

What is the relationship between the angles formed by two intersecting chords?

Back

The angles formed by two intersecting chords are related to the arcs they intercept; specifically, the measure of each angle is half the sum of the measures of the intercepted arcs.

Front

What is the power of a point theorem?

Back

The power of a point theorem states that for a point outside a circle, the product of the lengths of the segments of any secant line through the point is equal to the square of the length of the tangent segment from that point to the circle.