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Let $ABCD$ be a concave quadrilateral where $B$ is the reflex angle and $D$ is the opposite angle.Let the length of segments $AB$ and $BC$ be $10$ and the length of segments $AD$ and $CD$ be $15$. What's the length of the segment that would connect $B$ and $D$? I tried to make a kite and use the area of the kite to find the area of the concave quadrilateral but I didn't succeed. Thanks!

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    $\begingroup$ The length $BD$ can be anything between $5 = 15-10$ and $5\sqrt{8} = \sqrt{15^2-10^2}$. The second limit is the value where the quadrilateral fails to be concave. $\endgroup$ – achille hui Apr 3 at 18:49
  • $\begingroup$ @achillehui this was actually a question I was given and I haven't been able to solve it. So the question doesn't have a definite answer? P.S You have written 5 = 15 - 5 but I think you meant 5 = 15 -10:) $\endgroup$ – user531192 Apr 3 at 18:51
  • $\begingroup$ oops, typos. should be $5 = 15-10$ $\endgroup$ – achille hui Apr 3 at 18:52

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