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Angles and Segments
Inscribed angles are angles whose vertex is in the circle and the
sides contain chords of the circle.
Theorem:
The measure of an inscribed angle is equal to half of the measure
of its intercepted arc.
Corollary 1:
If two inscribed angles intercept the same arc, then the angles
are congruent.
Corollary 2:
If a quadrilateral is inscribed in a circle, then the opposite
angles of the quadrilateral are supplementary.
Corollary 3:
An angle inscribed in a semicircle is a right angle.
Theorem:
The measure of the angle formed by a chord and a tangent is equal to
half the measure of the intercepted arc.
Theorem:
The measure of an angle formed by two intersecting chords inside
a circle is equal to half the sum of the measures of the
intercepted arcs.
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