MathDB
Putnam 1958 February B1

Source: Putnam 1958 February

July 18, 2022
PutnamgeometryTriangles

Problem Statement

i) Given line segments A,B,C,DA,B,C,D with AA the longest, construct a quadrilateral with these sides and with AA and BB parallel, when possible. ii) Given any acute-angled triangle ABCABC and one altitude AHAH, select any point DD on AHAH, then draw BDBD and extend until it intersects ACAC in EE, and draw CDCD and extend until it intersects ABAB in FF. Prove that ∠AHE=∠AHF\angle AHE = \angle AHF.
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