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Incenter, parrllel

Source: 2021 Taiwan APMO Preliminary First Round

November 21, 2020
geometryincenterparallelogram

Problem Statement

(a) Let the incenter of △ABC\triangle ABC be II. We connect II other 33 vertices and divide △ABC\triangle ABC into 33 small triangles which has area 2,32,3 and 44. Find the area of the inscribed circle of △ABC\triangle ABC. (b) Let ABCDABCD be a parallelogram. Point E,FE,F is on AB,BCAB,BC respectively. If [AED]=7,[EBF]=3,[CDF]=6[AED]=7,[EBF]=3,[CDF]=6, then find [DEF].[DEF]. (Here [XYZ][XYZ] denotes the area of XYZXYZ)
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