The posted problem is virtually the same as the following:
The length of minor arc AB is twice the length of minor arc BC and the length of minor arc AC is three times the length of minor arc AB. What is the measure of angle BCA? (Please refer to the attachment)
1)20
2)30
3)40
4)50
5)60
An inscribed angle is formed by two chords.
Thus, angle BCA is an inscribed angle.
AB is the arc intercepted by inscribed angle BCA.
The degree measurement of an inscribed angle = 1/2 * the degree measurement of the arc intercepted by the inscribed angle.
Thus, angle BCA = (1/2)(arc AB).
Let BC = 1.
Since AB is twice BC, AB = 2.
Since AC is three times AB, AC = 3*2 = 6.
Thus, AB/circumference = 2/(1+2+6) = 2/9.
Since the circle = 360 degrees, the degree measurement of AB = (2/9)360 = 80.
Thus, angle BCA = (1/2)(arc AB) = (1/2)80 = 40.
The correct answer is
C.
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struggled a lot.. things don't seem to get into this hard matter.
