The length of the line that connects two opposite vertices in a concave quadrilateral

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!

• 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. – achille hui Apr 3 at 18:49
• @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:) – user531192 Apr 3 at 18:51
• oops, typos. should be $5 = 15-10$ – achille hui Apr 3 at 18:52