Circles: Secant, Tangent, and Chord Lengths

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 and is perpendicular to the radius at that point.

Front

What is a secant line?

Back

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

Front

Define a chord in a circle.

Back

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

Front

What is the relationship between the radius and the tangent line 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 chord given the radius and the distance from the center to the chord?

Back

Use the formula: length of chord = 2 * √(r² - d²), where r is the radius and d is the distance from the center to the chord.

Front

What is the standard equation of a circle with center (h, k) and radius r?

Back

(x - h)² + (y - k)² = r².

Front

In the equation (x+2)²+(y-3)²=4, what does the number 4 represent?

Back

The number 4 represents the square of the radius of the circle, so the radius is 2.

Front

How do you determine if a line is a tangent using the Pythagorean Theorem?

Back

If the square of the length of the tangent segment equals the square of the radius minus the square of the distance from the center to the line, then the line is a tangent.

Front

What is the length of a tangent segment from a point outside the circle to the point of tangency?

Back

The length of the tangent segment can be found using the formula: length = √(d² - r²), where d is the distance from the point to the center and r is the radius.

Front

Write the equation of a circle with center (7, 0) and radius 3.

Back

(x - 7)² + y² = 9.