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In a circle, the major arc is 3 times the minor arc. The corresponding central angles and the degree measures of two arcs are - Mathematics

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 3x and respectively.

 So             3x + x = 360

                         4x = 360

                            x = 90

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

 

  Is there an error in this question or solution?
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APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 15 Circles
Q 10 | Page 110
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