Segments of Circles: Tangents, Secants, Chords

Front

What is a segment of a circle?

Back

A segment of a circle is the region enclosed by a chord and the arc that connects the endpoints of the chord.

Front

Define a tangent to a circle.

Back

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

Front

What is a secant line?

Back

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

Front

Explain the relationship between a tangent and a radius at the point of tangency.

Back

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

Front

What is a chord in a circle?

Back

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

Front

State the Tangent-Secant Theorem.

Back

The Tangent-Secant Theorem states that if a tangent and a secant are drawn from a point outside a circle, then the square of the length of the tangent segment is equal to the product of the lengths of the secant segment and its external part.

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 formula for the area of a segment of a circle?

Back

Area of a segment = Area of the sector - Area of the triangle formed by the radius and the chord.

Front

Define the term 'arc' in relation to circles.

Back

An arc is a portion of the circumference of a circle.

Front

What is the relationship between the angles formed by two chords that intersect inside a circle?

Back

The measure of the angle formed by two intersecting chords is equal to the average of the measures of the arcs intercepted by the angle and its vertical angle.