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Raadsel: cirkel zagen - Weet Magazine - Raadsel november Skip to main content

Ik heb een driehoekig stuk spaanplaat overgehouden. Het heeft een omtrek van 21 dm, de oppervlakte is 21 dm2. Ik kan er niet zoveel mee, dus ik besluit er een cirkel uit te zagen. Wat is de diameter van de grootste cirkel die ik uit de plaat kan halen?

Section

Teken vanuit het middelpunt van de cirkel (waarvan we de straal r noemen) lijnen naar elk van de hoekpunten van de driehoek. Zo ontstaan er drie kleinere driehoeken. De oppervlakte van de onderste driehoek is de helft van “basis × hoogte”, dus: ½ × a × r. De oppervlakte van de grote driehoek is dus te schrijven als: ½ × r × (a + b + c). En dat is weer: ½ × r × omtrek!

Aangezien omtrek en oppervlakte in getalswaarde gelijk zijn (beide 21), is de conclusie dat r = 2 dm. De diameter van de cirkel is dus 4 dm, ofwel 40 cm.