# Is it impossible to construct an equilateral triangle inside a semicircle?

I have made it in a circle(which is very easy)....but I have been unable to make one inside a semicircle....is it not possible to make equilateral triangle inside a semicircle ?... If yes how can we prove it (please give the proof or the steps I need to take to prove it) ...? If no can anyone give me some examples of such equilateral triangle/semicircle.

Note: By constructing an equilateral triangle inside a semicircle I mean that all the vertices should lie on the arc(of the semicircle).

Edit: sorry for the confusion caused (I have deleted that comment )for this question the vertex cannot lie on the diameter..

• What exactly do you mean? Should all three vertices lie on the arc of the circle? – user296602 Dec 31 '15 at 8:28
• @user I have edited the question. – Freelancer Dec 31 '15 at 8:32
• Can a vertex lie on the diameter? – mrprottolo Dec 31 '15 at 8:34
• Vertices lying on the diameter is different than lying on the arc of the semicircle. Which do you want? – Teepeemm Dec 31 '15 at 13:08
• If one or two of the vertices may lie on the diameter then this is trivial: construct a circle, inscribe a hexagon in it, and take a pair of opposite vertices of the hexagon as the diameter of your semicircle, which now contains 3 (congruent) equilateral triangles. – PM 2Ring Dec 31 '15 at 13:21