Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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# Problem B. 4798. (May 2016)

B. 4798. In a cyclic quadrilateral $\displaystyle ABCD$, diagonals $\displaystyle AC$ and $\displaystyle BD$ are perpendicular, and the centre of the circumscribed circle is $\displaystyle K$. Prove that the areas of triangles $\displaystyle ABK$ and $\displaystyle CDK$ are equal.

(4 pont)

Deadline expired on June 10, 2016.

### Statistics:

 104 students sent a solution. 4 points: 101 students. 3 points: 1 student. 2 points: 1 student. 0 point: 1 student.

Problems in Mathematics of KöMaL, May 2016