Consider the cyclic quadrilateral with sides 1, 4, 8, 7 in that order. What is its circumdiameter?
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 20190315 13:03:51 