01 Minimum distance between projection points on the legs of right triangle

Problem
From the right triangle ABC shown below, AB = 40 cm and BC = 30 cm. Points E and F are projections of point D from hypotenuse AC to the perpendicular legs AB and BC, respectively. How far is D from AB so that length EF is minimal?
 

030-projections-of-d.gif

 

Solution

 
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