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B. 4737. $\displaystyle D$ is the foot of the altitude drawn to the hypotenuse $\displaystyle AB$ of a right-angled triangle $\displaystyle ABC$. The angles bisectors of $\displaystyle \angle ACD$ and $\displaystyle \angle BCD$ intersect hypotenuse $\displaystyle AB$ at $\displaystyle E$ and $\displaystyle F$, respectively. Determine the ratio of the inradius of triangle $\displaystyle ABC$ to the circmradius of triangle $\displaystyle CEF$.

Proposed by B. Bíró, Eger

(5 points)

Deadline expired on 10 November 2015.

Statistics on problem B. 4737.
 114 students sent a solution. 5 points: 79 students. 4 points: 15 students. 3 points: 6 students. 2 points: 6 students. 1 point: 2 students. 0 point: 1 student. Unfair, not evaluated: 3 solutions. Unfair, not evaluated: 2 solutions.

• Problems in Mathematics of KöMaL, October 2015

•  Támogatóink: Morgan Stanley