bob012345's latest activity

Trigonometric proof ##\theta +\varphi=90^{\circ}## Therefore ##\tan\theta=\cot\varphi\implies \tan\theta \tan\varphi=1.##...

##r^{2}=h^{2}+\left(r-a\right)^{2}\Rightarrow h^{2}=2ar-a^{2}=a\left(2r-a\right)=ab\Rightarrow h=\sqrt{ab}\quad\blacksquare##

In the figure below of a semi-circle, show that ##h=\sqrt{ab}##. In the special case where ##a=1## unit length, then ##h=\sqrt{b}##. A...

Is this the third solution you had in mind?

I understood its importance after solving it. A key is a key is a key. :oldsmile: I looked for other solutions, but I did not find any...

You nailed it! Did the clue help?

Before I just give the answer, I offer a clue in the form of a riddle. The key to unlocking this mystery is persistence.

I constructed a physical paper model. What I said in post #15 was wrong. I can't do this puzzle.

Can you describe the cut using the coordinate system I suggested above?

Well, it’s been 2 days and no one has offered up a different solution than the one above by @kuruman which I believe is the simplest...

BTW, if we label the bottom left corner of the original figure as (0,0) and the upper right corner as (5,3), we can describe the cut...

That gives what I showed in post #8. But there is at least one other solution. Who can find it and possibly more?

Yes.