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A chord is 2cm from the centre of a circle. If the radius of the...

Mathematics
WAEC 2013
A chord is 2cm from the centre of a circle. If the radius of the circle is 5cm, find the length of the chord
  • A. 2\(\sqrt{21}\)cm
  • B. \(\sqrt{42}\)cm
  • C. 2\(\sqrt{19}\)cm
  • D. \(\sqrt{21}\)cm
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Correct Answer: Option A
Explanation
From \(\bigtriangleup\) OMQ find /MQ/ by Pythagoras OQ2 = OM2 + MQ2

52 = 22 + MQ2

25 = 4 + MQ2

25 - 4 = MQ2

21 - MQ2

MQ2 = 21

MQ2 = \(\sqrt{21}\)

Length of chord = 2 x \(\sqrt{21}\) = 2\(\sqrt{21}\)cm
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