Circles and inscribed angles

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Circles and inscribed angles

• An inscribed angle is an angle whose vertex is on
  a circle and whose sides contain chords of the
  circle

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Intercepted arc

• The arc formed by an inscribed angle is the
  intercepted arc of that angle. Arc AC is the
  intercepted arc of angle ABC

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Theorem 47-1

• The measure of an inscribed angle is equal to
  half the measure of its intercepted arc
• mlt ABC 1/2 m arc AC

50o
25o
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Theorem 47-2

• If an inscribed angle intercepts a semicircle,
  then it is a right angle

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Proving and applying inscribed angle theorem

• 1) name inscribed angle
• 2) name arc intercepted by it
• 3) if mlt COD 52,
• find m ltCBD

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Finding angle measures in inscribed triangles

• Find the measures of the 3 angles in the triangle

90o
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Theorem 47-3

• If 2 inscribed angles intercept the same arc,
  then they are congruent

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Theorem 47-4

• If a quadrilateral is inscribed in a circle, then
  it has supplementary opposite angles.

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Finding angle measures in inscribed quadrilaterals

• ltA 4z ,
• lt C 3z5
• Find ltC

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