Geometry · Cyclic polygon · Inscribed angle · Thales theorem · Isosceles trapezoid · Pythagorean theorem
The points \(A, B, C, D, E\) lie on one circle in such a way that \(A\) and \(D\) are on opposite sides of the line \(BC\), and \(B\) and \(E\) are on opposite sides of the line \(CD\). Given that
\[ \angle ABC = \angle BCD = \angle CDE = 45^\circ , \]
prove that \(AB^2 + CD^2 = BC^2 + DE^2\).
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Serbian Regional Competition (Okruzno takmicenje) 2001, high school grade I, category A, problem 4. Organized by the Mathematical Society of Serbia (DMS). Source