Circle Tangents

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

How do you calculate the perimeter of a circle?

Back

The perimeter of a circle, also known as the circumference, can be calculated using the formula C = 2πr, where r is the radius of the 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

If two tangent segments are drawn from a point outside the circle, what can be said about their lengths?

Back

The lengths of the two tangent segments from a point outside the circle to the points of tangency are equal.

Front

What is the formula for the length of a tangent segment from a point outside the circle?

Back

The length of a 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.

Front

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

Back

To determine if a line segment is tangent to a circle, check if it meets the circle at exactly one point and if the radius to that point is perpendicular to the segment.

Front

What is the significance of the point of tangency?

Back

The point of tangency is significant because it is the only point where the tangent line touches the circle, and it defines the relationship between the circle and the tangent.

Front

What is the difference between a secant line and a tangent line?

Back

A secant line intersects a circle at two points, while a tangent line touches the circle at exactly one point.

Front

How can you find the length of a tangent segment if you know the radius and the distance from the center to the external point?

Back

Use the formula: length = √(d² - r²), where d is the distance from the external point to the center and r is the radius.

Front

What is the role of the radius in determining the properties of tangents?

Back

The radius helps determine the angle of intersection with the tangent line and confirms the perpendicular relationship at the point of tangency.