U10L2 Angles and Circles

Inscribed Angle

An angle whose vertex is on a circle and whose sides contain chords of the circle

Intercepted Arc

Lies in the interior of an inscribed angle

Measure of an Inscribed Angle Theorem

If an angle is inscribed in a circle, then its measure is half the measures of its intercepted arc.

Triangle Inscribed in a Semicircle Theorem

A triangle is inscribed in a semicircle if and only if it is a right triangle.

Inscribed Quadrilateral Theorem

A quadrilateral can be inscribed in a circle if and only if its opposite angles are supplementary.

Tangent and Chord Angles Theorem

If a tangent and a chord intersects to form an angle, then the measure of each angle is half the measure of the intercepted arc.

Chord Angles Theorem

If two chords intersect to form an angle, then the measure of each angle is half the sum of its intercepted arcs.

Secant Angles Theorem

If two secants intersect outside a circle to form an angle, then the measure of each angle is half the difference of its intercepted arcs.

Tangent Angles Theorem

If two tangents or a tangent and a secant intersect outside a circle to form an angle, then the measure of each angle is half the difference of the measures of its intercepted arcs.