Suppose we have a circle inscribed within a square. Now suppose a rectangle extends from one corner of the square to a point on the circle (see diagram).
If this rectangle is 6 inches by 12 inches, what is the radius of the circle in inches?
Solution
If we put the circle at the origin its equation would be
ReplyDelete$latex x^2+y^2=r^2$
the coordinate of the corner of the rectangle touching the circle would then be.
$latex -r + 12, r-6$
If we now substitute those coordinates in the circle equation we get
$latex (r-6)^2+(12-r)^2=r^2$
expanding and solving for r we get
$latex r^2-36 r+180=0$
giving r = 6 or 30 and clearly it can't be 6, so we get r=30 inches
Paul.