MCQ

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 3*x* and *x *respectively.

So 3x + x = 360

4x = 360

x = 90

So m \[\stackrel\frown{AB}\] = 90° and m \[\stackrel\frown{AB}\] = 3*x* = 270°

Is there an error in this question or solution?

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