Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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# Problem C. 1254. (December 2014)

C. 1254. In a triangle $\displaystyle ABC$, $\displaystyle T$ is the foot of the altitude drawn from $\displaystyle C$, and $\displaystyle AT=3BT$. Let $\displaystyle F$ denote the midpoint of $\displaystyle AB$, and let $\displaystyle D$ denote the point of altitude $\displaystyle CT$ where $\displaystyle AB$ subtends a right angle. Prove that if the orthocentre of triangle $\displaystyle ABC$ coincides with the centroid of triangle $\displaystyle FBD$ then $\displaystyle AD$ bisects the angle $\displaystyle BAC$.

(5 pont)

Deadline expired on January 12, 2015.

### Statistics:

 117 students sent a solution. 5 points: 76 students. 4 points: 17 students. 3 points: 11 students. 2 points: 7 students. 1 point: 5 students. 0 point: 1 student.

Problems in Mathematics of KöMaL, December 2014