MathDB

2

Part of 2016 239 Open Mathematical Olympiad

Problems(2)

angle $ARC$ is obtuse.

Source: 2016 239 S2

10/11/2020
In triangle ABCABC, the incircle touches sides ABAB and BCBC at points PP and QQ, respectively. Median of triangle ABCABC from vertex BB meets segment PQP Q at point RR. Prove that angle ARCARC is obtuse.
geometry
triangles $BTP$ and $DTQ$ are similar

Source: 2016 239 J2

10/11/2020
In a convex quadrilateral ABCDABCD rays ABAB and DCDC intersect at point PP, and rays BCBC and ADAD at point QQ. There is a point TT on the diagonal ACAC such that the triangles BTPBTP and DTQDTQ are similar, in that order. Prove that BD∥PQBD \Vert PQ.
geometry