Question 111

In a circle with center at O (0,0) and radius 5cm, AB is a chord of length 8 cm. If OM is perpendicular to AB, then the length of OM is:

Solution

Given : AB = 8 cm and OB = 5 cm

To find : OM = ?

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

=> AM = BM = $$\frac{1}{2}$$ AB

=> BM = $$\frac{8}{2}=4$$ cm

In $$\triangle$$ OBM,

=> $$(OM)^2=(OB)^2-(BM)^2$$

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

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

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

=> Ans - (A)

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