Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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# Problem A. 621. (September 2014)

A. 621. In an acute triangle $\displaystyle ABC$, the feet of the altitudes are $\displaystyle A_1$, $\displaystyle B_1$ and $\displaystyle C_1$, respectively. The midpoint of the side $\displaystyle BC$ is $\displaystyle F$. The circle $\displaystyle BCB_1C_1$ intersects the line segment $\displaystyle AA_1$ at point $\displaystyle D$. Let $\displaystyle T$ be that point on the line segment $\displaystyle DF$ for which the line $\displaystyle BT$ is tangent to the circle $\displaystyle AB_1C_1$. Let the line segment $\displaystyle C_1F$ meet the lines $\displaystyle BD$ and $\displaystyle BT$ at $\displaystyle P$ and $\displaystyle Q$, respectively. Show that the quadrilateral $\displaystyle DPQT$ has an inscribed circle.

(5 pont)

Deadline expired on October 10, 2014.

### Statistics:

 7 students sent a solution. 5 points: Fehér Zsombor, Saranesh Prembabu, Shapi Topor, Szabó 789 Barnabás, Williams Kada. 1 point: 1 student. 0 point: 1 student.

Problems in Mathematics of KöMaL, September 2014