SOLUTION: A circular fish pond is to be built in one corner of a rectangular shaped patio of dimensions 8 feet by 10 feet. The pond has a diameter of 6 feet. What is the shortest possible di
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Question 953363: A circular fish pond is to be built in one corner of a rectangular shaped patio of dimensions 8 feet by 10 feet. The pond has a diameter of 6 feet. What is the shortest possible distance (to the nearest tenth) between the edge of the pond and the corner of the patio nearest the pond? Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website! the pond is pressed against the vertical edge of the rectangle and the horizontal edge of the rectangle.
the intersection of the radius of the pond with the sides of the rectangle will be perpendicular to the edges of the rectangle.
what it appears you are talking about is the hypotenuse of a 45 degree right triangle that has 2 sides of 3.
the length of the hypotenuss is equal to sqrt(3^2+3^2) = sqrt(18) which can be simplified to 3 * sqrt(2).
since the radius of the pond is 3, then the difference between that and the edge of the rectangle is equal to 3*sqrt(2) - 3 which is equal to 1.242640687.
round that to the nearest tenth and you get 1.2 feet.
that looks like the minimum distance.
a picture of your pond inside the rectangle is included below for your reference.
what i think happens is:
the radii of the circle intersects with the vertical and horizontal sides of the rectangle forming tangents at those points which are perpendicular to the radii.
a 3 inch square is formed.
the diagonal of the 3 inch square is the hypotenuse of a right triangle that has 45 degrees as the acute angles.
the 45 degree acute angles that form the bottom triangle are:
angle BDC and angle CBD.
the hypotenuse of that right triangle is DB, the length of which is equal to sqrt(3^2 + 3^2) which is equal to sqrt(18).
sqrt(18) is equal to 4.2426... which is rounded to 4.2.
since the radius of the circle is on the hypotenuse as well, the difference between the length of the radius and the length of the diagonal of the square is 4.2 - 3 = 1.2.
1.2 is the minimum distance from the circle to the corner of the square.
the circle is equivalent to the edge of the pond.
calculations above the picture and below the picture are done differently but yield the same answer, as they should.
