Free · Algebra and geometric relations

Circle Angles, Chords, Secants and Tangents

Apply six circle relations, including central angles and a tangent through a coordinate point.

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Enter the known values in the units shown. Results update as you type.
Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
Use the worked example to check the method. Reset restores the starting fields.

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For the worked example, Central angle θ꜀ = 60.

Central angle=2×inscribed angle; chord²=4(r²−d²); PA×PD=PB×PC

Enter these known values and leave the other values blank.

Central and inscribed angles must subtend the same arc. Arc length uses radians.
For intersecting secants, all distances start at their common exterior point. A tangent coordinate lies on a circle centered at the origin.
The tangent slope is −x/y; y=0 gives a vertical tangent instead of a finite slope.

Choose the relevant mode and enter independent known quantities. Leave a missing value empty where the control permits an inverse.

The result follows the stated mathematical model. All dimensions must use consistent units; available unit selectors handle conversions.

Bookify validates the real geometric or algebraic domain and inverse branches omitted or approximated by this capture.