MHB In the triangle ABC the point D lies on the side BC and point E on the side AB

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In the triangle ABC the point D lies on the side BC and point E on the side AB. BD = AC, AD = AE and AB ^ 2 = AC * BC. Show that \angle BAD = \angle CEAView attachment 4777
 

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Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...

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