# Answer to the second challenge by Anthony OR - GGG 2015

Problem: Inscribe an equilateral triangle in a given triangle . Solutions: For any equilateral triangle a rotation with center one of the vertices and angle will map one of the remaining vertices onto the third vertex. Let point be an arbitrary point on segment .
• Drag the slider to the end to rotate segment on angle around point .
If vertex is on segment , then the third vertex should be on the image of , but it also has to be on the segment . Therefore, vertex is the intersection point of the segments and . This determines the side of the equilateral triangle.
• Click on the Construction button to finish the construction.
• When this problem has a solution?
• Drag point D on segment AB. Notice the relation between the intersecting points of the circle and the position of D.
• Drag the vertices of the triangle. Construct triangles for which the circle and segment BC have one intersection point.
A geometric construction using this transformation was first described by I. M. Yaglom, in Geometric Transformations I, MAA, 1962, Chapter 2, Problem 18