Triangles in Circles

Geometry Level 2

Rutwik was doodling around in math class and drew the two circles as shown in the diagram.

After giving it a thought Rutwik came up with a hypothesis and calls it \(Rutwik's \ Hypothesis\).

Here's his hypothesis.

Rutwik's Hypothesis : The \(GREEN\) triangle and the \(BLUE\) triangle are similar if and only if the segment \(a\) is parallel to segment \(b\).

What do you think about his hypothesis ?

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