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

Correct Answer: A. 2\(\sqrt{21}\)cm

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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