H2-13 tangents, central and inscribed angles

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• Tangents,
• Central
• And
• Inscribed angles

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• Two Tangents from the same point create congruent
  segments from that point to the points of
  tangency.

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• 1. Circle O is inscribed in triangle
• ABC. What is the triangles
• Perimeter?
• Since AD and AF both come from
• The same point A and are tangent, AD?AF
• We can find each of the missing segments this way
• Perimeter AD BD BE CE CF AF
• Perimeter 10 15 15 8 8 10
• Perimeter 66

10cm
15cm
8cm
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• 2. The inscribed circle has
• points of tangency at X, Y and Z.
• PX?PZ and RZ ? RY and QY ? QX
• Perimeter 15 15 17 17 4 4
• Perimeter 72 cm

15cm
17cm
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A
B
A central angle vertex is the center of a circle.
An arc the points that make up a portion of the
circumference of a circle.
P
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Minor arcs may be named by two points. Major arcs
and semicircles must be named by three
points. The length of an arc may also be
measured.
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Minor arc , 44
Minor arc , 36
Minor arc , 44
Major arc , 316
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Minor arc , 44
Minor arc , 36
Minor arc , 44
Major arc , 316
Minor arc , 136
Semi Circle, 180
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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 consists of endpoints
that lie on the sides of an inscribed angle and
all the points of the circle between them. A
chord or arc subtends an angle if its endpoints
lie on the sides of the angle.
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(No Transcript)
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½ ABC
2?ABC
2?QPR
½ 62
2113
236
31
226
72
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7. Finding Measures of Arcs and Inscribed Angles
Find each measure.
m?PRU
Inscribed ? Thm.
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7. Finding Measures of Arcs and Inscribed Angles
Find each measure.
Inscribed ? Thm.
Substitute 27 for m? SRP.
Multiply both sides by 2.