Intersecting Chords Theorem

This is the idea (a,b,c and d are lengths):

Intersecting chords

And here it is with some actual values (measured only to whole numbers):

chords example

And we get

Very close! If we measured perfectly the results would be equal.


Why not try drawing one yourself, measure the lengths and see what you get?


Why is this true?

Because there are similar triangles! Looking below:

Intersecting chords reason

The triangles may not be the same size, but they have the same angles ... so all lengths will be in proportion!

One triangle has the ratio a/c, and the other has the matching ratio d/b:

a/c = d/b

a × b = c × d