I'm struggling to find the radius of the circle in the image (the only other given length is the length between B and the right angle below, which is 5). Is it even possible to get the radius without knowing any other dimensions? Or is there a way to find it? I've tried to use Pythagoras but without knowing the length of the side of the triangle going towards O, it was hard to find it. enter image description here

  • $\begingroup$ Where have the 2.8s come from in your diagram? $\endgroup$ – mrnovice Feb 23 '17 at 22:00
  • $\begingroup$ It was given in the problem, where they asked to get the angle that I marked as theta. $\endgroup$ – Estermont Feb 23 '17 at 22:05
  • $\begingroup$ Just to clarify then, everything in the diagram you provided is from the question itself? $\endgroup$ – mrnovice Feb 23 '17 at 22:05
  • $\begingroup$ Yes I think so.The only information that I didn't put was 5 m (between point B and the right angle below it). $\endgroup$ – Estermont Feb 23 '17 at 22:09
  • $\begingroup$ Well I'm almost done, just need to find the angle PBO, if you have any ideas $\endgroup$ – mrnovice Feb 23 '17 at 22:22

There is no way to find $\theta$ or the radius from the given data. To see why, imagine to move point $P$ to the left on the horizontal line and let $O$ be the center of circle $ABP$: all given lengths would stay the same, but $r$ and $\theta$ would change.

enter image description here

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    $\begingroup$ This seems to be the problem posed by Regiomontanus. It has sense if he wants the radius for the greatest visual angle. $\endgroup$ – cgiovanardi Feb 25 '17 at 4:04
  • $\begingroup$ Thank you for reminding me of that.The angle of course is maximum when the radius is minimum, that is when the circle is tangent to the base line ($r=7,8$ m). $\endgroup$ – Aretino Feb 25 '17 at 8:52
  • $\begingroup$ Does that mean that the radius would be 7 or 8 m when the angle is maximized? $\endgroup$ – Estermont Feb 25 '17 at 12:35
  • $\begingroup$ Sorry, I should have written $r=7.8$ m. That is: when the circle is tangent, the radius is equal to the distance of $O$ from the baseline. $\endgroup$ – Aretino Feb 25 '17 at 12:43

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