Five circles

On the line segment CD = 6 there are 5 circles with radius one at regular intervals. Find the lengths of the lines AD, AF, AG, BD, and CE

Correct result:

d = 4.5826
f = 2.1794
g = 3.1225
b = 3.6056
c = 2.6458

Solution:

r = 1 h = v (A, C D) A S_{1} S_{2} = Δ 1 - 1 - 1, α = β = γ = 6 0^{\circ}, h = \sqrt{3} / 2 \cdot r = \sqrt{3} / 2 \cdot 1 ≐ 0.866 x_{1} = (4 + 1 / 2) \cdot r = (4 + 1 / 2) \cdot 1 = \frac{9}{2} = 4.5 d = ∣ A D ∣ d = \sqrt{x_{1}^{2} + h^{2}} = \sqrt{4. 5^{2} + 0.86 6^{2}} = \sqrt{21} = 4.5826

f = ∣ A E ∣ x_{2} = 4 / 2 \cdot r = 4 / 2 \cdot 1 = 2 f = \sqrt{x_{2}^{2} + h^{2}} = \sqrt{2^{2} + 0.86 6^{2}} = 2.1794

g = ∣ A G ∣ x_{3} = 6 / 2 \cdot r = 6 / 2 \cdot 1 = 3 g = \sqrt{x_{3}^{2} + h^{2}} = \sqrt{3^{2} + 0.86 6^{2}} = 3.1225

b = ∣ B D ∣ x_{4} = 7 / 2 \cdot r = 7 / 2 \cdot 1 = \frac{7}{2} = 3.5 b = \sqrt{x_{4}^{2} + h^{2}} = \sqrt{3. 5^{2} + 0.86 6^{2}} = \sqrt{13} = 3.6056

c = ∣ C E ∣ x_{5} = 5 / 2 \cdot r = 5 / 2 \cdot 1 = \frac{5}{2} = 2.5 c = \sqrt{x_{5}^{2} + h^{2}} = \sqrt{2. 5^{2} + 0.86 6^{2}} = \sqrt{7} = 2.6458

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