Subcontests
(4)Geometry
Given is triangle ABC with arbitrary point D on AB and central of inscribed circle I. The perpendicular bisector of AB intersects AI and BI at P and Q, respectively. The circle (ADP) intersects CA at E, and the circle (BDQ) intersects BC at F and (ADP) intersects (BDQ) at K. Prove that E,F,K,I lie on one circle. Inequality
Given are real numbers a1,a2,...,a101 from the interval [−2,10] such that their sum is 0. Prove that the sum of their squares is smaller than 2020.