Angle Relationships in Circles

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 and does not cross the circle.

Front

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

Back

The angle formed between a tangent line and a radius drawn to the point of tangency is always 90 degrees.

Front

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

Back

An inscribed angle is half the measure of the intercepted arc.

Front

If two chords intersect inside a circle, how do you find the measure of the angles formed?

Back

The measure of each 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 relationship between the angles formed by two secants that intersect outside a circle?

Back

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

Front

If a circle has a central angle of 80 degrees, what is the measure of the arc it intercepts?

Back

The measure of the intercepted arc is equal to the measure of the central angle, so it is also 80 degrees.

Front

What is the formula for finding 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 through the point of contact is equal to half the measure of the intercepted arc.

Front

How do you find the value of x in angle relationships involving circles?

Back

Use the properties of angles, such as the relationships between inscribed angles, central angles, and angles formed by tangents and chords.

Front

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

Back

The angles formed by two intersecting chords are equal to half the sum of the measures of the arcs intercepted by the chords.

Front

If a tangent and a secant intersect at a point outside the circle, how do you find the angle?

Back

The angle is equal to half the difference of the measures of the intercepted arcs.