Per7: Segment Relationships in Circles and Equation of a circle

Front

What is a circle?

Back

A circle is a set of points in a plane that are equidistant from a fixed point called the center.

Front

What is the standard equation of a circle?

Back

The standard equation of a circle with center (h, k) and radius r is (x-h)² + (y-k)² = r².

Front

What does the center of a circle represent?

Back

The center of a circle is the point from which all points on the circle are equidistant.

Front

How do you find the radius of a circle from its equation?

Back

In the equation (x-h)² + (y-k)² = r², the radius r is the square root of the constant on the right side.

Front

What is the diameter of a circle?

Back

The diameter of a circle is twice the radius and is the longest distance across the circle.

Front

What are segment relationships in circles?

Back

Segment relationships in circles refer to the relationships between different segments (chords, tangents, secants) and their lengths.

Front

What is a chord in a circle?

Back

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

Front

What is a tangent to a circle?

Back

A tangent is a line that touches the circle at exactly one point.

Front

What is a secant line?

Back

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

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