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Where is the center? (Posted on 2019-03-15) Difficulty: 3 of 5
Consider the cyclic quadrilateral with sides 1, 4, 8, 7 in that order. What is its circumdiameter?

No Solution Yet Submitted by Danish Ahmed Khan    
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Some Thoughts How my method must have gone wrong | Comment 2 of 3 |
Correction to the correction: apparently my solution did not fall into the category of error, as mentioned in the subsequent post by armando. sqrt(65) is in fact correct.

I assumed that the four angles whose sines are half of each given chord divided by the radius must add up to pi radians (half a circle). Now I see that could go awry if all the chords are on one side of the circle: my "solution" had been (and again, is):

arcsin(.5/r) + arcsin(2/r) + arcsin(4/r) + arcsin(3.5/r) = pi

Wolfram Alpha solves as r = sqrt(65)/2, therefore D = sqrt(65).

Edited on March 16, 2019, 8:23 am
  Posted by Charlie on 2019-03-15 13:03:51

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