Intercircle Quadrangle Calculator

Name: Intercircle Quadrangle - Geometry Calculator
Author: Jürgen Kummer

Calculations at an intercircle quadrangle. This is related to an interarc quadrangle, with the difference, that the straight lines are between different semicircles. So the most narrow section is not at the vertices, but within the curved edges.
Enter two of the three values from circle radius, distance of the centers and distance between the circles, as well as two of the three values from height of the first and second line and height of the interarc quadrangle. Choose the number of decimal places, then click Calculate.

Construction of an intercircle quadrangle.

Formulas:

a = b + 2 r

h = i + j

l = 2 \cdot (r - \sqrt{r^{2} - i^{2}}) + b

m = 2 \cdot (r - \sqrt{r^{2} - j^{2}}) + b

α = asin (\frac{i}{r}) + asin (\frac{j}{r}), α in rad

n = α \cdot r

k = r \cdot [1 - \cos (\frac{α}{2})]

s = 2 \cdot \sqrt{2 \cdot r \cdot k - k^{2}}

p = l + m + 2 n

A = \frac{(l + m) \cdot h}{2} - r \cdot n + s \cdot (r - k)

Radius, heights, lengths and perimeter have the same unit (e.g. meter), the area has this unit squared (e.g. square meter).

Since the intercircle quadrangle, unlike the interarc quadrangle, extends beyond the straight line connecting the two circle centers, it can be subdivided into two interarc quadrangles by precisely this line. These resulting quadrangles may be of equal or unequal size. The maximum intercircle quadrangle is formed when i=j=r, that is, when the straight edges of this shape lie upon two opposing tangents to the two circles.
The intercircle quadrangle possesses four internal angles ranging between 0 and 90 degrees. An angle of 90 degrees occurs when one of the two straight edges lies upon the line passing through the two circle centers. An angle of 0 degrees occurs when one or both edges lie upon a tangent common to both circles.
The intercircle quadrangle is axially symmetric with respect to the perpendicular line bisecting both straight edges. In the specific case where l=m, it possesses an additional axis of symmetry along the straight line passing through the two circle centers. In this instance, it is also centrally symmetric with respect to the point of intersection of the two axes of symmetry, and rotationally symmetric under a rotation of 180 degrees and multiples thereof.

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