Question 125

A chord of the larger among two concentric circles is of length 10 cm and it is tangent to the smaller circle. What is the area (in cm$$^2$$) of the annular portion between the two circles?

Solution

The two concentric circles with centre O and chord of larger circle AB = 10 cm and OD is the perpendicular bisector of AB

In right $$\triangle$$ BOD,

=> $$(OD)^2+(BD)^2=(OB)^2$$

=> $$R^2-r^2=(5)^2=25$$

Area of the portion between the circles = $$\pi R^2-\pi r^2$$

= $$\pi (R^2-r^2)=25\pi$$ $$cm^2$$

=> Ans - (B)

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