SOLUTION: The circles are concentric. The inner circle is shaded. The cord is tangent to the inner circle and has length 12. What is the area of the non-shaded region?

Question 452537: The circles are concentric. The inner circle is shaded. The cord is tangent to the inner circle and has length 12. What is the area of the non-shaded region?
Found 2 solutions by MathLover1, pedjajov:
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!

all you can do is state that:
Area of non shaded region = area of bigger circle - area of smaller circle. The cord is irrelevant in this case.
Answer by pedjajov(51) (Show Source): You can put this solution on YOUR website!
When you draw a picture you get that tangent touches inner circle and intersects with the outer circle.
:
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:
, where P is Pi.

:
So non shaded are is:

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.
:
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.
:
Now we can form Pythagorean theorem for this triangle as:

:
If we replace this into formula for area A we have

RELATED QUESTIONS
Two concentric circles are drawn so that the inner circle is shaded. The shaded area is... (answered by josgarithmetic)
Two concentric circles are shown. The radius of the inner circle is 3, and the distance... (answered by Fombitz)
There are two circles, one circle is inscribed and another circle is circumscribed over a (answered by ajmisra)
Diagram of circle with outer edge shaded. The outer circle has diameter 8 inches. The... (answered by josgarithmetic,MathTherapy)
[ Find the area enclosed between two concentric circles of radii 6.3 cm and 8.4 cm. A... (answered by TimothyLamb)
Both circles have the same center. The circumference of the inner circle is 12.56... (answered by Alan3354)
In a larger shaded circle, there are two smaller circles. The large circle has a diameter (answered by ikleyn)
A circle has a chord of length 8 that is tangent to a smaller, concentric circle. Find... (answered by scott8148)
Two concentric circles have radii of 16 cm and 34 cm. Find the length of the chord of... (answered by josgarithmetic)