SOLUTION: A circle passes through A and B, and its tangent to CD. Find its area, in cm^2. Diagram: https://imgur.com/a/XZgTPss''. Can I have an illustrated diagram to go with solution.

Algebra ->  Circles -> SOLUTION: A circle passes through A and B, and its tangent to CD. Find its area, in cm^2. Diagram: https://imgur.com/a/XZgTPss''. Can I have an illustrated diagram to go with solution.      Log On


   

Question 1151255: A circle passes through A and B, and its tangent to CD. Find its area, in cm^2.
Diagram: https://imgur.com/a/XZgTPss''.
Can I have an illustrated diagram to go with solution.
Found 2 solutions by pavan sai reddy, greenestamps:
Answer by pavan sai reddy(3) About Me  (Show Source):
Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


I'll let you draw the diagram, since I don't know how to include one with my response.

Since the circle passes through A and B, the center of the circle lies on the perpendicular bisector of AB.

Sketch the circle with center O passing through A and B, tangent to CD at E.

Let F be the midpoint of AB, and draw segment EF, which is part of the perpendicular bisector of AB. Note that the given information tells us the length of EF is 10.

Draw segment OB; then OFB is a right triangle.

Let r be the radius of the circle.

Segment EF, with length 10, is the sum of segments OE and OF. OE is a radius with length r; and OF is a leg of a right triangle with hypotenuse r and other leg 2.

Then....

10+=+r+%2B+sqrt%28r%5E2-2%5E2%29
10+=+r%2Bsqrt%28r%5E2-4%29
10-r+=+sqrt%28r%5E2-4%29
%2810-r%29%5E2+=+r%5E2-4
100-20r%2Br%5E2+=+r%5E2-4
100-20r+=+-4
104+=+20r
r+=+104%2F20+=+5.2

The radius of the circle is 5.2. Use that in the formula for the area of a circle and express the answer in the required form.