Mathematical and Physical Journal
for High Schools
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Problem B. 4738. (October 2015)

B. 4738. \(\displaystyle C\) is an arbitrary point of a circle \(\displaystyle k\) of diameter \(\displaystyle AB\), different from \(\displaystyle A\) and \(\displaystyle B\). Drop a perpendicular from \(\displaystyle C\) onto diameter \(\displaystyle AB\). The foot of the perpendicular on line segment \(\displaystyle AB\) is \(\displaystyle D\), and the other intersection with the circle \(\displaystyle k\) is \(\displaystyle E\). The circle of radius \(\displaystyle CD\) centred at \(\displaystyle C\) intersects circle \(\displaystyle k\) at points \(\displaystyle P\) and \(\displaystyle Q\). Let \(\displaystyle M\) denote the intersection of line segments \(\displaystyle CE\) and \(\displaystyle PQ\). Dertermine the value of \(\displaystyle \frac{PM}{PE} + \frac{QM}{QE}\).

Proposed by B. Bíró, Eger

(4 pont)

Deadline expired on November 10, 2015.


102 students sent a solution.
4 points:90 students.
3 points:5 students.
2 points:1 student.
1 point:5 students.
0 point:1 student.

Problems in Mathematics of KöMaL, October 2015