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Inscribed Angles Notes and Examples
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Vocab: inscribed angle
-an angle whose vertex is on a circle and whose sides are chords <ABC and <DEF are inscribed angles in the circles shown below: <ABC intercepts minor arc AC <DEF intercepts major arc DGF *intercept means “forms”
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Theorem 12-9: Inscribed Angle Theorem
The measure of an inscribed angle is equal to half of its intercepted arcs. C B
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Examples Find m<ABC Find m<ABC and m<ABD
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Examples Find m<DEF and mAEC Find m<ABC
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3 inscribed < corollaries (thm sheet)
If two inscribed angles intercept the same arc, then the angles are congruent. An angle inscribed in a semicircle is a right angle. If a quadrilateral is inscribed in a circle, then its opposite angles are supplementary.
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Theorem 12-10 The measure of an angle formed by a chord and a tangent is equal to half the measure of the intercepted arc. B B D D C C
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Ex: find the numbered angles.
1 108˚ 32˚ 1 2 1 2 102˚ 1 61˚ 46˚
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