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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