The question is as follows:

Let WISH be a cyclic quadrilateral, and K be the intersection of its diagonals WS and HI. Given that arc WI is 100 degrees and arc SH is 80 degrees, find the sizes of as many angles in the figure as you can.

I am really stuck in this problem. I am not sure whether K is the radius of the circle because it is the intersection of the diagonals. I just need a start, but I don't where to start. Any help will be really appreciated.

  • 2
    $\begingroup$ Hint: $\;WS \perp IH\,$ by the secant angle formula . $\endgroup$ – dxiv Sep 17 '17 at 3:54
  • $\begingroup$ @dxiv I see why $WS \perp IH$ through the secant formula (I learned a new topic!). However, I don't understand how to now find the $m \angle WOH$ or $m \angle WHO$, where $O$ is the center of the circle. It looks like as if line $WO$ and line $IO$ are congruent, but are they? $\endgroup$ – geo_freak Sep 17 '17 at 4:42
  • $\begingroup$ Assuming $O$ is the center of the circle, you can't determine $\,\angle WOH\,$ from just the given conditions. Imagine $\,WI\,$ and $\,SH\,$ are of fixed length, and you "slide" $\,SH\,$ around the circle. You'll get a family of quadrilaterals which all satisfy the given conditions, but have diiferent $\,\angle WOH\,$ angles. $\endgroup$ – dxiv Sep 17 '17 at 4:47
  • $\begingroup$ OK, thank you so much for the help! $\endgroup$ – geo_freak Sep 17 '17 at 4:54

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.