Trivia

Subject:
Re: Friday Puzzler -- Circle's radius

Larry Barrett
So continuing with this line of thinking, the total length of the horizontal chord is 8 and the the midpoint is at 4 (length of the chord from the midpoint to each end is 4). Similarly, for the vertical chord, the midpoint is at 3.5.Since the chords are perpendicular, we can construct a rectangle where the SW corner is where the chords intersect and the NE corner is at the center of the circle. The sides of the rectangle are .5 by 2.

Using Pythagoras, we can see that R^2 = 3.5^2 + 2^2 = 49/4 + 4 = 65/4.
So R = (sqrt65)/2.
Alternatively, R^2 = 4^2 + .5^2 = 16 + 1/4 = 65/4 and R = (sqrt65)/2.

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