Wikipedia:Reference desk/Archives/Mathematics/2021 October 11

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October 11

Geometry problem, acceptable solution?

In this problem: "given a circle with a diameter marked on it,j and a point on the circle, can you find a way to draw a line from the point that hits the diameter at a right angle." and considering the "restriction not to allow measuring devices, which means that you cannot use a compass or a marked ruler. All you are allowed is an unmarked ruler to draw straight lines."

For visualizing it: [1]

For the whole story: Guardian article with a link to a solution.

Would this also be a possible and acceptable solution:

• draw tangents touching the three given points
• mark the two points where the tangents of the points marked on the diameter intercept the tangent of the point on the circle.
• connect these two points to the points marked on the diameter.
• draw the line.

--Bumptump (talk) 17:16, 11 October 2021 (UTC)

@Bumptump: I'm afraid it's not acceptable. Classic constructions do not allow 'drawing a tangent'. A line can be drawn through any two known points. So you'd have to find (construct) another point on a tangent prior to drawing the line. --CiaPan (talk) 19:58, 11 October 2021 (UTC)