find the area of shaded region , given 2 concentric circles and AB is tangent to small circle having length of 20cm????

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