The angle of intersection of two straights is 120°. Find the ratio of the length of long chord to the tangent length.

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SSC JE Civil 10 Oct 2023 Shift 1 Official Paper-I
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  1. \(\sqrt 3\)
  2. 0.866
  3. 1/\(\sqrt 3\)
  4. 1

Answer (Detailed Solution Below)

Option 1 : \(\sqrt 3\)
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Concept

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Tangent length(T) = Rtan(Δ/2)
Length of curve(L) = πRΔ/180
Long chord(l) = 2Rsin(Δ/2)
External distance(E) = R(sec(Δ/2)-1)
Mid-ordinate(m) = R(1 - cos(Δ/2))

Given:

Angle of intersection = 120 °
Calculation:

we need to find deflection Angle = Δ
Angle of intersection + Deflection angle = 180°
∴ Deflection angle, Δ = 60°
Length of long chord(l) = 2 × R × sin (60°/2) = 2 × R × 1/2 = R.
Tangent length(T) = Rtan(60/2)\({R \over \sqrt 3}\)

\({l \over T} = {R \over R /\sqrt 3} = \sqrt 3\) (Ans)

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