A regular pentagon is inscribed in an ellipse with semi major axis 10 units. Then sum of all possible measures of the semi minor acis of the ellipse adds up to.

I don't exactly understand it. How to do?

  • 1
    $\begingroup$ If I get the problem correctly, you're expected to determine all possible positions of the pentagon inscribed in an ellipse with semi major axis measure $10$ and for each position find a semi minor axis length. Then sum semi minor axes lengths for all ellipses found. $\endgroup$ – CiaPan Dec 19 '17 at 16:10
  • $\begingroup$ Of course this could only make sense if the number of possible semi-minor axis values is finite. $\endgroup$ – hardmath Dec 19 '17 at 16:46

Five points determine a conic, so the "ellipse" is a circle.

  • $\begingroup$ I don't understand actually. After that? $\endgroup$ – Mathejunior Dec 19 '17 at 16:01
  • $\begingroup$ How to do the possible sum $\endgroup$ – Mathejunior Dec 19 '17 at 16:01
  • $\begingroup$ Well, the minor axis and the major axis of a circle are equal. They are radii, really. So there is only one possible legth for the minor axis. $\endgroup$ – ajotatxe Dec 19 '17 at 16:01
  • $\begingroup$ So it's 5? Right? $\endgroup$ – Mathejunior Dec 19 '17 at 16:04
  • $\begingroup$ Am I correct? I don't exactly understand. $\endgroup$ – Mathejunior Dec 19 '17 at 16:08

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