Intersecting Chords Theorem
What is the intersecting chords theorem
| chord_1_seg_1 | * | chord_1_seg_2 | = | chord_2_seg_1 | * | chord_2_seg_2 |
When we have a circle and we draw two chords that intersect
within that circle, let's call them chord_1 and chord_2,
our intersection point will create four line segments by dividing each chord into two segments.
The lengths of chord_1's segments multiplied will be equal to
the lengths of chord_2's segments multiplied.
This theorem holds no matter at what point the chords intersect.
Why Does it Work
When we construct triangles based on the intersecting chords we find that the created triangles are proportional
to one another.
Knowing that, it is simple to see why the theorem works.
Let's view the sides of the triangles as fractions, knowing that the fractions are proportional,
we can cross multiply and our products will be the same, thus proving the theorem.
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