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The Chords Corresponding to Congruent Arcs Are Congruent

The angles su...

Question

The angles subtended by arc XY and MN on the centre of the circle are 45° each. The length of the chord XY = 18 cm. What is the length of the chord MN? [3 Marks]

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Solution

[1 Mark]
Angle of arc XY = Angle subtended by the chord XY on the centre of the circle = 45°
Angle of arc MN = Angle subtended by the chord MN on the centre of the circle = 45°

XY = MN [If the angles subtended by the chords of a circle at the centre are equal, then the chords are equal] [1 Mark]

$∴$ MN = 18 cm [1 Mark]

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The Chords Corresponding to Congruent Arcs Are Congruent

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