Mathematical and Physical Journal
for High Schools
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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.


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 solutions.

Problems in Mathematics of KöMaL, October 2015