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fixed length wanted, circle passing through 2 fixed points

Source: China Northern MO 2013 p3 CNMO

October 28, 2022
geometryfixed

Problem Statement

As shown in figure , A,BA,B are two fixed points of circle āŠ™O\odot O, CC is the midpoint of the major arc ABAB, DD is any point of the minor arc ABAB. Tangent at DD intersects tangents at A,BA,B at points E,FE,F respectively. Segments CECE and CFCF intersect chord ABAB at points GG and HH respectively. Prove that the length of line segment GHGH has a fixed value. https://cdn.artofproblemsolving.com/attachments/9/2/85227f169193f61e313293e9128f6ece2ff1f7.png
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