Question
Download Solution PDFThe angle of intersection of two straights is 120°. Find the ratio of the length of long chord to the tangent length.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept
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)
Last updated on Jul 1, 2025
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