MathDB
Easy Geometry

Source: 2024 KJMO first round

October 27, 2024
geometrycircumcircle

Problem Statement

There is a △ABC\triangle ABC which ∠C=90\angle C=90, and ABˉ=36\bar{AB}=36 On the circumcircle of △ABC\triangle ABC, there is \overarc{BC} which does not include point AA. D is on \overarc{BC}. It satisfies 2×∠CAD=∠BAD2\times\angle CAD = \angle BAD E:ADˉ∩BCˉE: \bar{AD}\cap\bar{BC} AEˉ=20 \bar{AE}=20 Find BDˉ2 \bar{BD}^2
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