Skip to content / Đến nội dung
ThichHocToan.com

MathNet 2018-part-02 — 181 problems (EN–VI) Question 108

Math Olympiad Vault · MathNet 2018-part-02 — 181 problems (EN–VI)

Question 108

Medians $AD$, $BE$, and $CF$ of triangle $ABC$ intersect at point $M$. Is it possible that the circles with radii $MD$, $ME$, and $MF$
a) all have areas smaller than the area of triangle $ABC$;
b) all have areas greater than the area of triangle $ABC$;
c) all have areas equal to the area of triangle $ABC$?