Circle Tangent Arrow Calculator

Name: Circle Tangent Arrow - Geometry Calculator
Author: Jürgen Kummer

Calculations at a circle tangent arrow. This occurs, when on a circle two intersecting tangent lines are drawn. These, together with the chord, form an isosceles triangle. For the circle tangent arrow, the circular segment is removed from this triangle.
Enter the lengths of the legs and the angle at the arrowhead. Choose the number of decimal places, then click Calculate. Angles are calculated and displayed in degrees, here you can convert angle units. The angle must be smaller than 180°.

α = 90 ° - \frac{β}{2}

Θ = 2 α

s = \frac{a \cdot \sin (β)}{\sin (α)}

r = \frac{s \cdot \sin (90 ° - α)}{\sin (Θ)}

h = r \cdot (1 - \cos (\frac{Θ}{2}))

i = \sqrt{\frac{(4 \cdot a^{2} - s^{2})}{4}} - h

l = r \cdot Θ (Θ in rad)

p = 2 a + l

A = \frac{[(i + r) \cdot s - r \cdot l]}{2}

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

This circle tangent arrow is concave. The convex variant, the drop shape, could also be called a circular tangent arrow. In this case, the corner points in the other direction.
The smaller the angle at the arrowhead, the longer the arrow is, the longer is its height i. If the angle of the circular tangent arrow is 90 degrees, meaning the triangle is isosceles and right, then a quarter circle is subtracted from the triangle. At an angle of 180 degrees, the circular tangent arrow becomes a point on the circle. At an angle of 0 degrees, a semicircle would be extended infinitely.
The circular tangent arrow has an axis of symmetry through the angle along the height i, which is the bisector of the arrowhead. This shape has no other symmetries.

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