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Question
In a circle, the major arc is 3 times the minor arc. The corresponding central angles and the degree measures of two arcs are
Options
90° and 270°
90° and 90°
270° and 90°
60° and 210°
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Solution
270° and 90°
We are given the major arc is 3 times the minor arc. We are asked to find the corresponding central angle.
See the corresponding figure.
We know that angle formed by the circumference at the centre is 360°.
Since the circumference of the circle is divided into two parts such that the angle formed by major and minor arcs at the centre are 3x and x respectively.
So 3x + x = 360
4x = 360
x = 90
So m \[\stackrel\frown{AB}\] = 90° and m \[\stackrel\frown{AB}\] = 3x = 270°
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