Warm up 30 80 100 180 100 260 . Inscribed Angles and Inscribed Quadrilaterals.
12.3 Inscribed Angles
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12.3 INSCRIBED ANGLESBrett Solberg AHS ‘11-’12
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WARM-UP
1) What is the measure of arc AC?
2) What is the arc length of arc AC?
3)
Get out your notes and HW.
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HW REVIEW
#8
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TODAY’S AGENDA
Quiz 12.3 Inscribed Angles
Last day for retakes
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QUIZ
3 Problems 6 minutes Use your notes Flip over when done
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1) Is BC tangent to circle a? How do you know?
2) What is the perimeter of the polygon?
3) Find the value of x.
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REVIEW
What is the difference between: arc length measure of an arc
Measure of an arc = measure of the central angle.
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INSCRIBED CIRCLE
Inscribed Angle Angle whose vertex is on a circle and whose
sides are chords. Intercepted arc
Arc created by an inscribed angle.
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EXAMPLE 1
Identify the inscribed angle and the intercepted arc.
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THEOREM 12.9-INSCRIBED ANGLE THEOREM
The measure of an inscribed angle is half the measure of its intercepted arc.
ABC = ½AC
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DEMONSTRATION
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EXAMPLE 2
Find the measure of arc AC
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EXAMPLE 2
Find the measure of arc PT and angle R.
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EXAMPLE 2
Find the measure of angle G and angle D.
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COROLLARIES TO THE INSCRIBED ANGLE THEOREM
1) Two inscribed angles that share an intercepted arc are congruent.
2) An angle inscribed by a semicircle is a right angle.
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COROLLARIES TO THE INSCRIBED ANGLE THEOREM
3) The opposite angles of a quadrilateral inscribed in a circle are supplementary.
angle N + angle O = 180˚ angle P + angle M = 180˚
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THEOREM 12.10
The measure of an angle formed by a tangent and a chord is half the measure of the intercepted arc.
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EXAMPLE 4
RS and TU are diameters of circle A. RB is tangent to circle A at point R. Find the measure of angle BRT and TRS.
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ASSIGNMENT
Worksheet 2.3
EC Assignment Due on THU pg. 711 #1 – 43 all