c^2

b^2

a^2

ABC = ACH + ABH \
⇒ ∃k/ \; k a^2 = k b^2 + k c^2  \
⇒ a^2 = b^2 + c^2

Nota:\; k∈(0, 1/4),  \pero  \; esto  \; no  \; es  \; relevante \  
en  \; la  \; demostración.

B = (-12.84, 2.56)
C = (-6.72, 2.58)
c_1 = Semicircle(B, C)
A = Point(c_1)
c = Segment(B, A)
b = Segment(A, C)
a = Segment(C, B)
i = OrthogonalLine(A, a)
H = Intersect(i, a)
j = Segment(A, H)
c2: {Polygon[A, B, 4]}
b2: {Polygon[C, A, 4]}
a2: {Polygon[B, C, 4]}
anima = 0.04 (slider from 0 to 1, step 0.01)
ABC: {Polygon[A, B, C]}
ABD: {Polygon[A, B, H]}
ACD: {Polygon[A, C, H]}