Segment Lengths & Angle Measures in Circles

Front

What is the definition of a tangent line in relation to a circle?

Back

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

Front

What is the relationship between the radius and a 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 tangent segment from a point outside the circle?

Back

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

Front

What is the measure of an angle formed by two tangents drawn from a point outside a circle?

Back

The measure of the angle formed by two tangents is equal to half the difference of the measures of the intercepted arcs.

Front

If two chords intersect inside a circle, how do you find the lengths of the segments?

Back

The products of the lengths of the segments of each chord are equal: (a)(b) = (c)(d), where a and b are segments of one chord and c and d are segments of the other.

Front

What is the formula for the measure of an inscribed angle in a circle?

Back

The measure of an inscribed angle is half the measure of the intercepted arc.

Front

How do you calculate the arc length of a circle?

Back

Arc length can be calculated using the formula: Arc Length = (θ/360) × 2πr, where θ is the central angle in degrees and r is the radius.

Front

What is the definition of a central angle in a circle?

Back

A central angle is an angle whose vertex is at the center of the circle and whose sides are radii that extend to the circle.

Front

What is the relationship between the central angle and the arc it intercepts?

Back

The measure of the central angle is equal to the measure of the arc it intercepts.

Front

How do you find the measure of an angle formed by a tangent and a chord?

Back

The measure of the angle formed by a tangent and a chord is equal to half the measure of the intercepted arc.