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Published byPierce Joseph Modified over 8 years ago
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Topic 12-3
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Definition Secant – a line that intersects a circle in two points.
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Definitions Inscribed angle – an angle whose vertex is on a circle and whose sides contain chords of the circle Intercepted arc – the arc that lies in the interior of an inscribed angle and has endpoints on the angle inscribed angle intercepted arc
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Example 1: Name ALL of the inscribed angles and their corresponding intercepted arcs below. Inscribed angles/Intercepted Arc: ____________________________ ____________________________ ____________________________
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Central Angle
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Measure of an Inscribed Angle Theorem If an angle is inscribed in a circle, then its measure is half the measure of its intercepted arc.
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Example 2: Given that m BC = 100 , find the value of ‘x’ in circle O x = _______________
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Try This!
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Try this!
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Congruent Inscribed Angles Theorem If two inscribed angles of a circle intercept the same arc, then the angles are congruent.
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Example 3: In circle Q, m ST = 68 . Find the m 1 and m 2. m 1 = _______________ m 2 = _______________
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Definitions Inscribed polygon – a polygon whose vertices all lie on a circle. Circumscribed circle – A circle with an inscribed polygon. The polygon is an inscribed polygon and the circle is a circumscribed circle.
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Inscribed Right Triangle Theorem If a right triangle is inscribed in a circle, then the hypotenuse is a diameter of the circle. The triangle is a right triangle and the angle opposite the diameter is the right angle.
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Example 5: In circle A, m 1 = (6x + 11) , m 2 = (9x + 19) , m 3 = (4y – 25) , m 4 = (3y – 9) , and PQ RS. Find m 1, m 2, m 3, m 4 m 1 = _______________ m 2 = _______________ m 3 = _______________ m 4 = _______________
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Inscribed Quadrilateral Theorem Opposite angles of an inscribed quadrilateral are supplementary.
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Example 6: Quadrilateral QRST is inscribed in circle C. If m T = 95 , m S = 100 , find m Q and m R m Q = __________ m R = __________
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Example 3 Find the value of each variable. a. b.
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