Geometry: An Interactive Journey to Mastery

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x Drawing in the radii to the endpoints of an arc marked with an angle measure can make a picture

overly complicated. Do this only if it seems truly helpful to make the central angle explicit.

 Complete the proof of the inscribed/central angle theorem by
showing that y = 2x in this picture of a central angle and an
inscribed angle on a common arc of a circle.
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 Find x, y, and z for the following circle with center O.
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 Two congruent circles with centers A and B each have radii
of 7 inches. If AB LQFKHV¿QGWKHOHQJWKRIWKHLU
common chord.
Hint: Draw a picture. Must the two circles intersect?
What must “common chord” mean?

 Circles with centers A and B are externally tangent with
point of contact Pͼ௘6HH)LJXUH௘ͽ
Explain why A, P, and B are sure to be collinear.

Problems

y x

Figure 19.14

y z x

O 40°

110°

Figure 19.15

P

A

B

Figure 19.16