### A Problem In an Isosceles Right Triangle: What is this about?

A Mathematical Droodle

What if applet does not run? |

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Copyright © 1996-2018 Alexander BogomolnyThe applet is supposed to suggest the following attractive fact (and its proof):

ABC is an isosceles right angled triangle with the right angle at C. Points D and E, equidistant form C, are chosen arbitrarily on AC and BC. Perpendiculars from D and C to AE meet the hypotenuse AB at K an L. Prove that |

What if applet does not run? |

To see why this is so, extend AC to AF with

### References

- R. Honsberger,
*Mathematical Delights*, MAA, 2004, pp.89-90 - V. V. Prasolov,
*Problems in Planimetry*, v 1, Nauka, Moscow, 1986, p. 30 (in Russian)

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Copyright © 1996-2018 Alexander Bogomolny