Question 72
A 5 cm long perpendicular is drawn from the centre of a circle to a 24 cm long chord. Find the diameter of the circle.
Solution
As shown in the figure,
Perpendicular OD bisects the chord AB
$$=$$> AD = BD = 12 cm
By the pythagoras theorem,
$$\text{OB}^2=12^2+5^2$$
$$=$$> $$\text{OB}^2=144+25$$
$$=$$> $$\text{OB}^2=169$$
$$=$$> $$\text{OB}=13$$
Radius of the circle (OB) = 13 cm
$$\therefore\ $$Diameter of the circle = 2 x 13 = 26 cm
Hence, the correct answer is Option A
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