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Computational Geo

Source: LIMIT 2020 Cat 1 Obj P13

May 2, 2020
geometrylimit

Problem Statement

On the side ACAC of an acute triangle △ABC\triangle ABC, a point DD is taken such that 2AD=CD=2,BD⊥AC2AD=CD=2, BD\perp AC. A circle of radius 22 passes through AA and DD and is tangent to the circumcircle of △BDC\triangle BDC. Find [Area(△ABC)][\text{Area}(\triangle ABC)] where [.][.] is the greatest integer function.
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