Line segments in Circles

Front

What is a tangent line in relation to a circle?

Back

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

Front

If QS is a tangent to circle P, what can be said about the radius at the point of tangency?

Back

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

Front

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

Back

Use the formula: length of tangent segment = √(distance from point to center² - radius²).

Front

What is the relationship between the lengths of two tangent segments drawn from the same external point?

Back

The lengths of the two tangent segments are equal.

Front

If a circle has a radius of 10 units, what is the length of a tangent segment from a point 15 units away from the center?

Back

Length of tangent segment = √(15² - 10²) = √(225 - 100) = √125 = 5√5 units.

Front

What is the formula for the perimeter of a circle?

Back

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

Front

If the radius of a circle is 7 units, what is the circumference?

Back

C = 2π(7) = 14π units.

Front

What is the definition of a secant line in relation to a circle?

Back

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

Front

How do you find the length of a secant segment?

Back

Use the formula: length of secant segment = √(external segment × total length of secant).

Front

What is the relationship between a tangent and a secant that intersect at a point outside the circle?

Back

The square of the length of the tangent segment is equal to the product of the lengths of the entire secant segment and its external segment.