Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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Problem B. 4778. (March 2016)

B. 4778. Let \(\displaystyle D\) denote an interior point of an acute-angled triangle \(\displaystyle ABC\). Construct the circles of diameters \(\displaystyle AD\), \(\displaystyle BD\) and \(\displaystyle CD\), and draw a tangent from each of the points \(\displaystyle A\), \(\displaystyle B\) and \(\displaystyle C\) to each of the two circles not passing through it. Prove that the sum of the squares of the six tangents equals the sum of the squares of the sides of the triangle.

(3 pont)

Deadline expired on April 11, 2016.


99 students sent a solution.
3 points:89 students.
2 points:9 students.
0 point:1 student.

Problems in Mathematics of KöMaL, March 2016