The figure shows two concentric circles. If the length of chord AB is 80 units and chord AB is tangent to the smaller circle, what is the area of the shaded region? Express your answer in terms of pi.

Guest Jun 29, 2018

#1**0 **

Let the midpoint of chord AB = D

Let the center of the larger circle =O

Connect AO and BO to form triangle ABO

Draw a perpendicular line from O to D

Now, you have 2 congruent right triangles with:

Angle OAB = OBA = 45 degrees

Cos(45) = 40/BA(Radius)

BA =56.568 - Radius of the large circle

Area =(56.568)^2 x Pi =~3200 pi

Tan(45) =DO(radius of the small circle) / 40

Radius = 40

Area of the smaller circle =40^2 x pi =1600 pi

**3200 pi - 1600 pi =1600 pi - ****area**** of the shaded region.**

Guest Jun 29, 2018