Topic 75 Angle Relationships in Circles

Front

What is the definition of an angle in a circle?

Back

An angle in a circle is formed by two rays (sides of the angle) that share a common endpoint (the vertex) and are drawn from the center of the circle to the circumference.

Front

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

Back

The measure of 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 measure of an inscribed angle in a circle?

Back

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

Front

What is the definition of a central angle?

Back

A central angle is an angle whose vertex is at the center of the circle and whose sides (rays) extend to the circumference.

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 through the point of contact is equal to half the measure of the intercepted arc.

Front

What is the relationship between the angles formed by two secants that intersect outside a circle?

Back

The measure of the angle formed by two secants that intersect outside a circle is equal to half the difference of the measures of the intercepted arcs.

Front

What is the definition of a cyclic quadrilateral?

Back

A cyclic quadrilateral is a four-sided figure where all vertices lie on the circumference of a circle.

Front

What is the relationship between the opposite angles of a cyclic quadrilateral?

Back

The opposite angles of a cyclic quadrilateral are supplementary, meaning they add up to 180 degrees.

Front

What is the formula for the sum of the interior angles of a polygon?

Back

The sum of the interior angles of a polygon with n sides is (n-2) × 180 degrees.

Front

What is the definition of a tangent to a circle?

Back

A tangent to a circle is a line that touches the circle at exactly one point and is perpendicular to the radius at that point.