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0632 geometry with tangential quadr. 6th edition Round 3 p2

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May 3, 2021
geometry6th edition

Problem Statement

Let ABCDABCD be a convex quadrilateral, and the points A1∈(CD)A_1 \in (CD), A2∈(BC)A_2 \in (BC), C1∈(AB)C_1 \in (AB), C2∈(AD)C_2 \in (AD). Let M,NM, N be the intersection points between the lines AA2,CC1AA_2, CC_1 and AA1,CC2AA_1, CC_2 respectively. Prove that if three of the quadrilaterals ABCDABCD, A2BC1MA_2BC_1M, AMCNAMCN, A1NC2DA_1NC_2D are circumscriptive (i.e. there exists an incircle tangent to all the sides of the quadrilateral) then the forth quadrilateral is also circumscriptive.
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