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(1998 KJMO P7) ADE is an isosceles triangle

Source: 1998 KJMO P7

June 30, 2024
geometrycircumcircleangle bisectorKJMO

Problem Statement

OO is a circumcircle of non-isosceles triangle ABCABC and the angle bisector of AA meets BCBC at DD. If the line perpendicular to BCBC passing through DD meets AOAO at EE, show that ADEADE is an isosceles triangle.
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