Question 5

AB is a chord of the circle and its center is “O”. OM is perpendicular to AB. If the length of AB=20 cm, OM = $$(2\sqrt11)$$ cm, find the radius (in cm) of the circle.

Solution

Given : OM is perpendicular to AB and OM = $$2\sqrt{11}$$ cm

Also, MB = $$\frac{20}{2}=10$$ cm

In right $$\triangle$$ MOB,

=> $$(OB)^2=(OM)^2+(MB)^2$$

=> $$(OB)^2=(2\sqrt{11})^2+(10)^2$$

=> $$(OB)^2=44+100=144$$

=> $$OB=\sqrt{144}=12$$ cm

=> Ans - (B)

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