# Intersecting Chords Theorem

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

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

And we get

- 71 × 104 =
**7384** - 50 × 148 =
**7400**

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:

- The angles θ are the same (see vertically opposite angles)
- The angles φ are the same (see inscribed angles)

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