6

Part of 1979 Poland - Second Round

Problems(1)

DL^2 + KC^2 = AB^2 , semicircle externally on a rectangle

Source: Polish MO Recond Round 1979 p6

\overline{DC}

of the rectangle

ABCD

\frac{AB}{AD} = \sqrt{2}

a semicircle is built externally. Any point

M

of the semicircle is connected by segments with

A

B

to obtain points

K

L

\overline{DC}

, respectively. Prove that

DL^2 + KC^2 = AB^2

geometrysemicirclerectangle