A chord of circle of radius 7cm is 5cm from the... - JAMB Mathematics 2011 Question
A chord of circle of radius 7cm is 5cm from the centre of the maximum possible area of the square?
A
4√6 cm
B
3√6 cm
C
6√6 cm
D
2√6 cm
correct option: a
From Pythagoras theorem
|OA|2 = |AN|2 + |ON|2
72 = |AN|2 + (5)2
49 = |AN|2 + 25
|AN|2 = 49 - 25 = 24
|AN| = \(\sqrt {24}\)
= \(\sqrt {4 \times 6}\)
= 2√6 cm
|AN| = |NB| (A line drawn from the centre of a circle to a chord, divides the chord into two equal parts)
|AN| + |NB| = |AB|
2√6 + 2√6 = |AB|
|AB| = 4√6 cm
|OA|2 = |AN|2 + |ON|2
72 = |AN|2 + (5)2
49 = |AN|2 + 25
|AN|2 = 49 - 25 = 24
|AN| = \(\sqrt {24}\)
= \(\sqrt {4 \times 6}\)
= 2√6 cm
|AN| = |NB| (A line drawn from the centre of a circle to a chord, divides the chord into two equal parts)
|AN| + |NB| = |AB|
2√6 + 2√6 = |AB|
|AB| = 4√6 cm
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