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Is it possible to draw an isosceles triangle with a compass and a ruler? The ruler is not marked, the two legs of the compass cannot leave the paper, and the two points on the plane are known.

**I mean the two points at the base of the isosceles triangle are already given. The legs of the isosceles triangle are not given. **

First draw a circle at one point, with the legs of the compass not leaving the paper, drag to another point, and then draw a second circle?

netF
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  • To my understanding, if the two legs of the compass cannot leave the paper, you can only draw one circle. Also, which two points are known? –  Mar 24 '20 at 15:07
  • I think OP means "you cannot lift the compass up". – Calvin Lin Mar 24 '20 at 15:08
  • Means the same thing. If the positioning of the compass cannot be changed, how can you ever draw more than one circle? – Andrew Chin Mar 24 '20 at 15:08
  • @CalvinLin what does "not lifting up the compass" mean, materially, if not what I said? –  Mar 24 '20 at 15:08
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    @Gae.S. I was trying to express that we we have a "collapsible compass". IE could use the compass via drawing arc/circles at multiple different centers, but cannot "bring along the distance draw to another circle with a distinct center". (I subsequantly realized we only need 1 circle to achieve this) – Calvin Lin Mar 24 '20 at 15:10
  • @CalvinLin Ah, I see the intention now. Quite a questionable exercise. –  Mar 24 '20 at 15:12
  • What do "the two points" refer to? Are you requiring that these two points be vertices of the triangle? Maybe you are even requiring that the two points be opposite the equal sides? – lulu Mar 24 '20 at 15:30
  • What is the "waist" of an isosceles triangle? – lulu Mar 24 '20 at 15:49
  • Move the compass to one of the given points. Make its aperture larger than half of the given segment. For example, the same as the given segment is larger than half of it. If the side of the isosceles triangle were given make it of that size. Draw a circle. Then move the compass to the other given point and without changing the aperture. Draw a circle. The two circles intersect at two points. Draw, with the ruler then lines joining these points to the two given points. Two triangles will appear, which are two solutions. –  Mar 24 '20 at 15:54
  • Sorry. I mean the two points at the base of the isosceles triangle are already given. – netF Mar 24 '20 at 15:59
  • Your stipulation about the 2 legs of the compass not leaving the paper is highly confusing. You can easily do this with a standard straight-edge and compass construction, by constructing the perpendicular bisector of the given line segment (the two given points of the base). Any point on that bisector wil be the apex of an isosceles triangle. But if you can't lift the compass up from one point and put it down on another, you can only make concentric circles, and I don't see a way to use that. Please be more precise about what you expect. – Deepak Mar 24 '20 at 16:00
  • The legs of the isosceles triangle are not given. – netF Mar 24 '20 at 16:10
  • @lulu The legs of the isosceles triangle are not given. – netF Mar 24 '20 at 16:12
  • @Deepak First draw a circle at one point, with the legs of the compass not leaving the paper, drag to another point, and then draw a second circle? – netF Mar 24 '20 at 16:30
  • @CalvinLin n First draw a circle at one point, with the legs of the compass not leaving the paper, drag to another point, and then draw a second circle? – netF Mar 24 '20 at 16:33

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