Point inside an equilateral triangle

ABC is an equilateral triangle. Point D is a point in the same plane and three segments are connected to it where each segment is perpendicular to a side of the triangle as shown.

This is a Java Applet created using GeoGebra from www.geogebra.org - it looks like you don't have Java installed, please go to www.java.com

1.) Move A or B to choose the size of the equilateral triangle.
2.) Move point D. What do you observe.
3.) Repeat 1 and 2 several times. Is your observation still the same?
4.) Make a conjecture about your observation and try to see if you can prove it.

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