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

- Author:
- Irina Boyadzhiev

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 .
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.

- Drag the slider to the end to rotate segment
on angle around point .

- 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.

*Geometric Transformations I*, MAA, 1962, Chapter 2, Problem 18