### Isosceles on the Sides of a Triangle: What is this about?

A Mathematical Droodle

What if applet does not run? |

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Copyright © 1996-2018 Alexander BogomolnyThe applet's purpose is to suggest the following statement:

On the sides of ΔABC erect isosceles triangles AFB, BDC, and CEA. Prove that the perpendiculars through A, B, C to EF, FD, DE, respectively are concurrent. |

What if applet does not run? |

### Proof

The proof is straightforward. Consider three circles cD, cE, cF centered at D, E, F with radii

### References

- R. Honsberger,
*Mathematical Delights*, MAA, 2004, pp. 19-20

### Radical Axis and Radical Center

- How to Construct a Radical Axis
- A Property of the Line IO: A Proof From The Book
- Cherchez le quadrilatere cyclique II
- Circles On Cevians
- Circles And Parallels
- Circles through the Orthocenter
- Coaxal Circles Theorem
- Isosceles on the Sides of a Triangle
- Properties of the Circle of Similitude
- Six Concyclic Points
- Radical Axis and Center, an Application
- Radical axis of two circles
- Radical Axis of Circles Inscribed in a Circular Segment
- Radical Center
- Radical center of three circles
- Steiner's porism
- Stereographic Projection and Inversion
- Stereographic Projection and Radical Axes
- Tangent as a Radical Axis
- Two Circles on a Side of a Triangle
- Pinning Butterfly on Radical Axes
- Two Lines - Two Circles
- Two Triples of Concurrent Circles
- Circle Centers on Radical Axes
- Collinearity with the Orthocenter
- Six Circles with Concurrent Pairwise Radical Axes
- Six Concyclic Points on Sides of a Triangle
- Line Through a Center of Similarity

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Copyright © 1996-2018 Alexander Bogomolny67566263