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Dana je kruznica k{O,r} a bod A, pricom |AO|=d < r. Dotycnice z bodu A sa kruznice k dotykaju v bodoch B,C. Trojuholniku ABC je vpisana kruznica . Vyjadrite jej polomer q pomocou danych usekoc d a r.
Nájdite najmenšie štvorciferné číslo abcd také, že rozdiel: (ab)2 – (cd)2 je trojciferné číslo zapísané tromi rovnakými ciframi. -Príklad číslo 1
2. Určte najväčší možný počet neprázdnych po dvoch disjunktných množín s rovnakými súčtami prvkov, na ktoré možno rozdeliť množinu a) {1,2,...,2017}, b) {1,2,....2018}. Ak je množina tvorená…
3. Daný je pravouhlý trojuholník ABC s preponou AB, v ktorom D onzačuje pätu výšky z vrcholu C. V polrovine s hraničnou priamkou AB a vnútorným bodom C uvažujme body E,F také, že uhly EBA, FAB sú…
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