Question : A chord of length 120 cm is at a distance of 32 cm from the centre of a circle. What is the radius (in cm) of the circle?
Option 1: 96
Option 2: 34
Option 3: 72
Option 4: 68
Correct Answer: 68
Solution :
A is the Centre of the circle.
Chord BC = 120 cm
AD is perpendicular to BC.
AD = 32 cm
$\therefore$ BD = $\frac{BC}{2}$ = $\frac{120}{2}$ = 60 cm
In $\triangle$ABD,
AD = 32 cm
BD = 60 cm
$\angle$ADB = 90°
So, AB $=\sqrt{60^2+ 32^2}=\sqrt{ 3600 + 1024}=\sqrt{4624}=68$ cm
$\therefore$ The radius of the circle = 68 cm
Hence, the correct answer is 68.
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