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
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
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
Source: Myschool Past Questions Archive (Record #36869)