find the area of shaded region

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Let the contact point of tangent be P...

Center of inner circle be O and one point of tangent at the outer circle be A

Then Triangle AOP will be a right angle triangle with angle APO = 90

By figure OA is radius of outer circle.

and OP is radius of inner circle...

Area of shaded region will be Area = pi[ (OA)^2 - (OP)^2] ----------(1)

Now Apply Pythagorus theorem in Triangle AOP we have...

(AO)^2 = (AP)^2 + (OP)^2

Now Complete Length of Tangent is given 20 so AP = 10 {because it is chord to outer circle}

(AO)^2 -(OP)^2 = (AP)^2 = 100

And from (1) we have area = pi [ 100] = 314 cm^2

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