I'll call the middle point M. Because of the Law of Sines, we must have \(\frac{\sin \angle EAM}{EM}=\frac{\sin \angle EMA}{EA}\), and also \(\frac{\sin \angle EDM}{EM}=\frac{\sin \angle EMD}{ED}\).

Rearranging and combining these, and using the fact that \(EA=ED\), we must have \(\frac{\sin \angle EMA}{\sin \angle EAM}=\frac{\sin \angle EMD}{\sin \angle EDM}\). This equation holds in the diagram on the left, but not on the right.
–
Matt Enlow
·
2 years, 10 months ago

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The point defined in the problem is uniquely determined. You cannot claim that \( \angle EDM \) is any arbitrary angle.

Note: I've cropped your image, so that the pentagons which you drew are now much larger.
–
Calvin Lin
Staff
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2 years, 10 months ago

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TopNewestI'll call the middle point

M. Because of the Law of Sines, we must have \(\frac{\sin \angle EAM}{EM}=\frac{\sin \angle EMA}{EA}\), and also \(\frac{\sin \angle EDM}{EM}=\frac{\sin \angle EMD}{ED}\).Rearranging and combining these, and using the fact that \(EA=ED\), we must have \(\frac{\sin \angle EMA}{\sin \angle EAM}=\frac{\sin \angle EMD}{\sin \angle EDM}\). This equation holds in the diagram on the left, but not on the right. – Matt Enlow · 2 years, 10 months ago

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The point defined in the problem is uniquely determined. You cannot claim that \( \angle EDM \) is any arbitrary angle.

Note: I've cropped your image, so that the pentagons which you drew are now much larger. – Calvin Lin Staff · 2 years, 10 months ago

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