SOLUTION: A circle with area 1369ℼ cm^2 passes through A and B, and is tangent to line CD. If {{{ x/y = 1/3 }}}, find y in cm. Diagram: https://imgur.com/gox1hfD (I tried my best to dra

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: A circle with area 1369ℼ cm^2 passes through A and B, and is tangent to line CD. If {{{ x/y = 1/3 }}}, find y in cm. Diagram: https://imgur.com/gox1hfD (I tried my best to dra      Log On

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Question 1189759: A circle with area 1369ℼ cm^2 passes through A and B, and is tangent to line CD. If +x%2Fy+=+1%2F3+, find y in cm.
Diagram: https://imgur.com/gox1hfD (I tried my best to draw in the circle)
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52778) About Me  (Show Source):
You can put this solution on YOUR website!
.

But the problem does not say that AB  is parallel to  CD.


Without it,  the problem can not be solved and is  DEFECTIVE.



Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


With an area of 1369ℼ, the radius of the circle is 37.

Let O be the center of the circle; let E be the point where the segment with length y in the diagram intersects CD; and let F be the point of tangency of the circle with line CD. Draw the diameter FG, intersecting AB at H.

The diameter FG is the perpendicular bisector of chord AB, so the length of GB is x/2. The given information x%2Fy=1%2F3 then tells us that EB/GB=6. So

Let GB = w
Then BE = 6w

Draw radius OB and look at right triangle OHB.

%28OH%29%5E2%2Bw%5E2=37%5E2
OH=sqrt%281369-w%5E2%29

Then we can see FH=EB=6w, so

37%2Bsqrt%281369-w%5E2%29=6w
sqrt%281369-w%5E2%29=6w-37
1369-w%5E2=%286w-37%29%5E2
1369-w%5E2=36w%5E2-444x%2B1369
37w%5E2-444w=0
37w%28w-12%29=0
w=12

y is the length of EB, which is 6w = 72.

ANSWER: y = 72 cm