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📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 Um den Umfang des Kreises zu finden, in den ein Quadrat mit einer Seitenlänge von 8 cm eingeschrieben ist, bestimmen wir zuerst den Durchmesser des Kreises. Bei einem Quadrat, das in einen Kreis eingeschrieben ist, ist der Durchmesser des Kreises gleich der Diagonale des Quadrats. Mit dem Satz des Pythagoras wird die Diagonale \(d\) des Quadrats wie folgt berechnet:

📌 d = \sqrt{8^2 + 8^2} = \sqrt{64 + 64} = \sqrt{128} = 8\sqrt{2} \text{ cm}.

📌 Der Umfang \(C\) des Kreises ist gegeben durch

📌 C = \pi \cdot d = \pi \cdot 8\sqrt{2} = 8\sqrt{2}\pi \text{ cm}.

📌 Somit ist der Umfang \(\boxed{8\sqrt{2}\pi}\) Sekundenlängen.

📌 Frage: Berechne \(\tan 75^\circ\) und gib deine Antwort in einfachster Radikalform.

📌 Um \(\tan 75^\circ\) zu berechnen, verwenden wir die Additionstheorem für Tangens:

📌 \tan(75^\circ) = \tan(45^\circ + 30^\circ) = \frac{\tan 45^\circ + \tan 30^\circ}{1 - \tan 45^\circ \tan 30^\circ}.

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