Tangent Lines and Chords of a Circle

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, known as the point of tangency.

Front

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

Back

The tangent line 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

What is the diameter of a circle?

Back

The diameter is a chord that passes through the center of the circle and is the longest chord.

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 does it mean for arcs to be congruent in a circle?

Back

Congruent arcs have the same measure and subtend congruent chords.

Front

If two chords are congruent, what can be said about their distances from the center of the circle?

Back

Congruent chords are equidistant from the center of the circle.

Front

What is the relationship between the angles formed by two intersecting chords in a circle?

Back

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

Front

What is the significance of the central angle in relation to chords and arcs?

Back

The central angle subtended by a chord is equal to the measure of the arc that the chord intercepts.

Front

How can you determine if two tangents drawn from a point outside the circle are equal?

Back

The lengths of the two tangents drawn from an external point to a circle are equal.