SOLUTION: A b c and d lie on a circle center O radius 8cm ab and cd are tangents to a circle center O radius 4cm abcd is a rectangle A) calculate the distance AE ? B)calculate the shaded

Question 1111019: A b c and d lie on a circle center O radius 8cm ab and cd are tangents to a circle center O radius 4cm abcd is a rectangle
A) calculate the distance AE ?
B)calculate the shaded area ?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
This post has at least two FATAL errors:

1)   The point E is not defined,   and

2)   The shaded area is not explained.

Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

The other tutor is right in that you have not given all the information that is required to answer the questions that are asked.

However, I see only one possible interpretation for each of the questions that is asked... so I will make a guess at solving the problem.

We have two concentric circles with center O, one with radius 4 and the other with radius 8. Rectangle ABCD is inscribed in the larger circle (its vertices are on the larger circle), with AB and CD tangent to the smaller circle.

You ask for the length of AE without defining point E. The only length AE we can determine from the given information is if E is the point where AB is tangent to the smaller circle. In that case, the radii of the two circles and the Pythagorean Theorem give us the length of AE as 4*sqrt(3).

You also ask for the area of the shaded region, without defining what that region is. Again I see only one possible interpretation -- that the area we want is the area of the annulus (the region between the two circles). With the radii of the two circles, that is easy to find: 64pi - 16pi = 48pi.

If the questions being asked were something different than that, then you need to re-post the question with all the required information.
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