You can see that the angle that is formed from the intersection of the chords is equal to

$$ \frac{a + b}{2} $$

This is true because this angle is the exterior angle of the triangle containing the green line. Use the fact that the exterior angle of a triangle is equal to the sum of the other two angles of the triangle.

The great thing about trying to prove why identities and theorem are true is that it helps you remember them, also. And it helps you to analyze new situations with a clever, creative approach. Great job on thinking about this idea!

Happy Learning,

The Daily Challenge Team

]]>So for any a and b, the angle of the intersection of the chords will always be a+b/2 no matter what size a and b are and no matter where the intersection is?

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