Fie paralelogramul

. Se alege un punct

exterior lui, astfel incat

. Aratati ca

.

[Citat] Fie paralelogramul . Se alege un punct exterior lui, astfel incat . Aratati ca .

Unghiurile sunt orientate?

Nu...

[Citat] Nu...

Dac? nu, problema e gre?it?:


Dac? lucr?m cu unghiuri orientate, e OK. Indica?ie: fie F astfel ca AEFD sa fie paralelogram. Atunci ?i BEFC este paralelogram, iar CDFE e inscriptibil.



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Va multumesc.

Enun?ul problemei ar fi trebuit formulat altfel, pentru a elemina ambiguit??ile:

în interiorul patrulaterului convex BCDE se consider? punctul A astfel ca ABCD s? fie paralelogram...etc

De curiozitate, care e sursa problemei?

2012/13 British Mathematical Olympiad
Round 2
1. Are there infinitely many pairs of positive integers (m, n) such that
both m divides n2 + 1 and n divides m2 + 1?
2. The point P lies inside triangle ABC so that < ABP = < PCA. The
point Q is such that PBQC is a parallelogram. Prove that < QAB =
< CAP.
3. Consider the set of positive integers which, when written in binary,
have exactly 2013 digits and more 0s than 1s. Let n be the number
of such integers and let s be their sum. Prove that, when written in
binary, n + s has more 0s than 1s.
4. Suppose that ABCD is a square and that P is a point which is on the
circle inscribed in the square. Determine whether or not it is possible
that PA, PB, PC, PD and AB are all integers.

[Citat] 2. The point P lies inside triangle ABC so that < ABP = < PCA. The point Q is such that PBQC is a parallelogram. Prove that < QAB = < CAP.

Da, în formularea asta lucrurile sunt clare.