inscribed angle
an angle whose vertex is on a circle and whose sides contain chords of the circle
Theorem 9-7
The measure of an inscribed angle is equal to half the measure of its intercepted arc.
Theorem 9-7 Corollary 1
If two inscribed angles intercept the same arc, then the angles are congruent.
Theorem 9-7 Corollary 2
An angle inscribed in a semicircle is a right angle.
Theorem 9-7 Corollary 3
If a quadrilateral is inscribed in a circle, then its opposite angles are supplementary.
Theorem 9-8
The measure of an angle formed by a chord and a tangent is equal to half the measure of the intercepted arc.
Theorem 9-9
The measure of an angle formed by two chords that intersect inside a circle is equal to half the sum of the measures of the intercepted arcs.
Theorem 9-10
The measure of an angle formed by two secants, two tangents, or a secant and a tangent drawn from a point outside a circle is equal to half the difference of the measures of the intercepted arcs.
Theorem 9-11
When two chords intersect inside a circle, the product of the segments of one chord equals the product of the segments of the other chord.
Theorem 9-12
When two secant segments are drawn to a circle from an external point, the product of one secant segment and its external segment equals the product of the other secant segment and its external segment.
Theorem 9-13
When a secant segment and a tangent segment are drawn to a circle from an external point, the product of the secant segment and its external segment is equal to the square of the tangent segment.