Segments of Circles: Tangents, Secants, Chords

Front

What is a tangent to a circle?

Back

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

Front

Define a secant line.

Back

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

Front

What is a chord in a circle?

Back

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

Front

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

Back

The length of the tangent segment can be calculated using the formula: length = √(distance from the point to the center of the circle² - radius²).

Front

What is the relationship between a tangent and a radius at the point of tangency?

Back

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

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

What is the formula for the area of a segment of a circle?

Back

The area of a segment of a circle can be calculated using the formula: Area = (r²/2)(θ - sin(θ)), where r is the radius and θ is the angle in radians.

Front

How do you find the angle formed by two chords that intersect inside a circle?

Back

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

Front

What is the relationship between the lengths of two chords that intersect inside a circle?

Back

If two chords intersect inside a circle, the products of the lengths of the segments of each chord are equal.

Front

Define the term 'arc' in relation to circles.

Back

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