Geometry and Progressions! :)

Geometry Level pending

In an isosceles right triangle, ABC,with the right angle at C, the length of a leg is 20 inches.Perpendiculars are dropped from C to the hypotenuse,from the foot of this perpendicular o leg CB,from the foot of this perpendicular to AB, then back to leg CB,etc. without end.Find the sum of the lengths of all the perpendiculars.

NOTE: write your answer in two four decimal places.

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