Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
 Already signed up? New to KöMaL?

# Problem B. 4737. (October 2015)

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 pont)

Deadline expired on November 10, 2015.

### Statistics:

 112 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 solutionss.

Problems in Mathematics of KöMaL, October 2015