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Inscribed Angles. May 13, 2008. What is an inscribed angle?. An inscribed angle is an angle whose vertex is on a circle and whose sides contain chords of the circle. We say that angle 1 above intercepts the arc shown in red. Measure of an inscribed angle.
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Inscribed Angles May 13, 2008
What is an inscribed angle? • An inscribed angle is an angle whose vertex is on a circle and whose sides contain chords of the circle. We say that angle 1 above intercepts the arc shown in red.
Measure of an inscribed angle • Theorem: The measure of an inscribed angle is equal to half the measure of its intercepted arc.
Proving the measure of an inscribe angle • Try this one…
1st Corollary • Corollary 1: If two inscribed angles intercept the same arc, then the angles are congruent.
2nd Corollary • Corollary 2: An angle inscribed in a semicircle is a right angle.
3rd Corollary • Corollary 3: If a quadrilateral is inscribed in a circle, then its opposite angles are supplementary.
Angles formed by a chord and a tangent • Theorem: The measure of an angle formed by a chord and a tangent is equal to half the measure of the intercepted arc.
More about chords • Theorem: 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.
Secants and tangent • Theorem: 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.
