MathDB

4

Part of 2005 JBMO Shortlist

Problems(1)

3 equal angles via projections on isosceles triangle

Source: JBMO Shortlist 2005

1/1/2018
Let ABCABC be an isosceles triangle (AB=AC)(AB=AC) so that ∠A<2∠B\angle A< 2 \angle B . Let D,ZD,Z points on the extension of height AMAM so that ∠CBD=∠A\angle CBD = \angle A and ∠ZBA=90∘\angle ZBA = 90^\circ. Let EE the orthogonal projection of MM on height BFBF, and let KK the orthogonal projection of ZZ on AEAE. Prove that ∠KDZ=∠KDB=∠KZB \angle KDZ = \angle KDB = \angle KZB.
geometryisoscelesequal angles