Question 452537
When you draw a picture you get that tangent touches inner circle and intersects with the outer circle.
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Area of non shaded area is a difference between areas of outer and inner circle.
If radius of inner circle is r1 and radius of outer circle is r2 we have:
{{{Ai=r1^2*P}}}, where P is Pi.
{{{Ao=r2^2*P}}}
:
So non shaded are is:
{{{A=Ao-Ai=(r2^2-r1^2)*P}}}

We have three points:
- point C for center of the circle(s)
- point A where tangent touches inner circle
- point B where tangent intersects outer circle
:
These three points connected form right triangle with legs CA and AB and hypotenuse CB.
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Leg CA is radius for inner circle r1.
Hypotenuse CB is radius for outer circle r2.
:Point A also divides tangent exactly at half so AB is 6.
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Now we can form Pythagorean theorem for this triangle as:
{{{r1^2+6^2=r2^2}}}
{{{r2^2-r1^2=36}}}
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If we replace this into formula for area A we have
{{{A=36*P}}}