Proof Length of Tangent Squared Equals Product of Chord With Chord Extended to Meet Tangent


The length of a tangent squared equals product of chord with chord extended to meet the tangent.


Draw chords AD and BD.

Now consider the trianglesand

Angleis common to both triangles, so call itCall anglethen other angles can be found in terms ofand

Now draw radii fromto the centre of the circle and label the remaining angles.


Hence trianglesare similar.


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