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Work Shown:
Given Info
arc BCD = 21
arc EF = 35 (this is the shortest distance along the circle from points E to F)
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Using arc EF, we can say that angle ECF is also the same measure. The central angle and the arc measure are always equal.
angle ECF = 35
Then using the vertical angle theorem, we can say that
angle ACB = angle ECF
angle ACB = 35
From the fact that central angle ACB is 35 degrees, we can then say minor arc AB is also 35 degrees
Through similar reasoning, minor arc BD = angle BCD = 21
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So we have
- minor arc AB = 21
- minor arc BD = 35
which add to
(minor arc AB)+(minor arc BD) = arc ABD
(21)+(35) = arc ABD
56 = arc ABD
arc ABD = 56
See the diagram below and hopefully it will clear up any confusion. The diagram is composed of two figures. Figure 1 shows how to get minor arc AB. Figure 2 shows how to get minor arc BD.
