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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. The length of the chord MN is
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. The length of the chord MN is
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Solution
The correct option is C 18 cm
We know,
Angle of an arc XY = Angle subtended by the chord XY with the centre of the circle = 45°
Angle of an arc XY = Angle subtended by the chord XY with the centre of the circle = 45°
By the theorem, we get
XY = MN = 18 cm
[Theorem: If the angles subtended by the chords of a circle at the centre are equal, then the chords are equal.]
We know,
Angle of an arc XY = Angle subtended by the chord XY with the centre of the circle = 45°
Angle of an arc XY = Angle subtended by the chord XY with the centre of the circle = 45°
By the theorem, we get
XY = MN = 18 cm
[Theorem: If the angles subtended by the chords of a circle at the centre are equal, then the chords are equal.]
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