Magyar Information Contest Journal Articles

# Problem C. 919. (November 2007)

C. 919. A right-angled triangle is cut into a triangle and a quadrilateral by the perpendicular bisector of its hypotenuse. The ratio of the diagonals of the quadrilateral is . Find the acute angles of the right-angled triangle.

(5 pont)

Deadline expired on December 17, 2007.

Sorry, the solution is available only in Hungarian. Google translation

Megoldás:

Mivel E rajta van az AB szakasz felező merőlegesén, ezért EBA=BAC=.

, ezért . A Thalesz-tétel miatt BD=DC, így az átlók aránya . Tudjuk, hogy , ezért az átlók aránya:

Mivel

ezért

=75o,

=15o.

### Statistics:

 274 students sent a solution. 5 points: 232 students. 4 points: 19 students. 3 points: 4 students. 2 points: 4 students. 1 point: 4 students. 0 point: 10 students. Unfair, not evaluated: 1 solution.

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