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.

### Statistics:

 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