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

Question 1189759: A circle with area 1369ℼ cm^2 passes through A and B, and is tangent to line CD. If , 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(52780) (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(13200) (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 then tells us that EB/GB=6. So

Let GB = w
Then BE = 6w

Draw radius OB and look at right triangle OHB.

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

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

ANSWER: y = 72 cm

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