Question 68

If the length of a chord of a circle is 16 cm and is at a distance of 15 cm from the centre of the circle, then the radius of the circle (in cm) is:

Solution

Given : AB = 16 cm and OC = 15 cm

To find : OB = $$r$$ = ?

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

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

=> BC = $$\frac{16}{2}=8$$ cm

In $$\triangle$$ OBC,

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

=> $$(OB)^2=(8)^2+(15)^2$$

=> $$(OB)^2=64+225=289$$

=> $$OB=\sqrt{289}=17$$ cm

=> Ans - (C)

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