The fundamentals of geometry of a circular curve those required to understand the fundamentals of laying out of a circular curve are as follows:

Rule 1 : The angle subtended by any chord at the centre of the circle is twice the angle between the chord and a tangent at one of its ends. For example, in Figure 37.4, the angle subtended by the chord AB at the centre of the circle, RAOB (d) is twice the angle RVAB between the chord AB and the tangent AV at end A (d / 2).

Rule 2 : Inscribed angles subtended by the same or equal arc or chord are equal. In Figure 37.4, inscribed angles at C and E subtended by the chord AB are equal and both are (d / 2).

Rule 3 : Inscribed angle subtended by the same or equal arc or chord is half the angle subtended (by the arc or chord) at the centre of the circle. In Figure 37.4, the inscribed angles at C and E (d / 2) is half the angle subtended by the chord AB at the centre of the circle, AOB (d).

Rule 4 : The deflection angle between a tangent (at any point on a circle) and a chord is equal to the angle which the chord subtends in the alternate segment. For example, in Figure 37.4, the deflection angle at D from the tangent at A (RVAD) is equal to the angle subtended by the chord AD at B (RABD) i.e., RVAD = RABD.

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