Measure of two ares formed by a chord of a circle are 2x and 7x find the measure of minor are

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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

•  90° and 270°

• 90° and 90°

•  270° and 90°

• 60° and 210°

 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°

Concept: Angle Subtended by an Arc of a Circle

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