A chord of circle of radius 7cm is 5cm from the centre of the circle.What is the length of the chord?
-
4√6 cm
- 3√6 cm
- 6√6 cm
- 2√6 cm
The correct answer is: A
Explanation
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
There is an explanation video available .