An inscribed angle is an angle formed by two chords in a circle which meet at a common point. This common endpoint forms the vertex of the inscribed angle. The other two endpoints of the chords define intercepted arc on the circle.
In the figure above ABC is an inscribed angle and AC is an inscribed arc.
Conjecture 1: In a circle, the measure of an inscribed angle is half the measure of the central angle with the same intercepted arc. (A central angle is any angle whose vertex is located at the center of a circle.)
angle ABC = 1/2 × angle AOC
Conjecture 2: In a circle, two inscribed angles with the same intercepted arc are congruent.
angle ABC = angleADC
Conjecture 3: Any angle inscribed in a semi-circle is a right angle.
angle ABC = 90°
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