Angles and Segments in Circles

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.

Front

What is the measure of an arc in a circle?

Back

The measure of an arc is the degree measure of the angle formed by two radii that connect the center of the circle to the endpoints of the arc.

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 Pythagorean theorem: if the distance from the point to the center is 'd' and the radius is 'r', then the length of the tangent 't' is given by t = √(d² - r²).

Front

What is the relationship between the angle formed by two tangents from a point outside the circle?

Back

The angle formed by two tangents from a point outside the circle is equal to half the difference of the measures of the intercepted arcs.

Front

What is the formula for the circumference of a circle?

Back

The circumference C of a circle is given by the formula C = 2πr, where r is the radius.

Front

How do you calculate the area of a sector of a circle?

Back

The area A of a sector is given by A = (θ/360) × πr², where θ is the angle in degrees and r is the radius.

Front

What is the inscribed angle theorem?

Back

The inscribed angle theorem states that an angle inscribed in a circle is half the measure of the intercepted arc.

Front

What is the central angle of 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

How do you find the measure of an angle formed by two chords intersecting inside a circle?

Back

The measure of the angle formed by two chords intersecting inside a circle is equal to half the sum of the measures of the intercepted arcs.

Front

What is the relationship between the lengths of tangents drawn from an external point to a circle?

Back

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