Question 126

The diameter of a circle is 10 cm. If the distance of a chord from the centre of the circle be 4 cm, then the length of the chord is

Solution

Given : OB is the radius of circle = 5 cm and OC = 4 cm

To find : AB = ?

Solution : The line from the centre of the circle to the chord bisects it at right angle.

=> AC = BC = $$\frac{1}{2}$$ AB

In $$\triangle$$ OBC,

=> $$(BC)^2=(OB)^2-(OC)^2$$

=> $$(BC)^2=(5)^2-(4)^2$$

=> $$(BC)^2=25-16=9$$

=> $$BC=\sqrt{9}=3$$ cm

$$\therefore$$ AB = $$2 \times$$ BC

= $$2 \times 3=6$$ cm

=> Ans - (A)

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