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Answer:
(1+√2)/2 ≈ 1.207 cm
Step-by-step explanation:
The angled flats are at 45°, so the length in the direction of a vertical or horizontal radius is (1 cm)/√2 = (1/2)√2 cm. The remaining length of that radius is half the length of a flat, so is 1/2 cm. The total length of the radius is ...
1/2 + 1/2√2 = (1+√2)/2 ≈ 1.207 cm
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In trigonometry terms, the length of the flat is ...
1 cm = 2(r)(tan(45°/2))
so the radius is ...
r = (1 cm)/(2·tan(22.5°))
r = (1/2)cot(22.5°) ≈ 1.207
