A semicircle and a circle are tangent. The tangency point is shown. Prove that the two coloured triangles are similar.

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## Solution

Note that this solution never uses the right angle at P. The prove therefore is also valid for non-diameter chords.

## Poem

As within so without

With a triangle in interactions

And power and responsability in connection

In this triangulation

Each one has a singular position

People seem not able to take decisions

In Karpmann’s triangle, it’s difficult to analyse

And to know well the motivations

## One reply on “As within, so without”

Absolutely so.

At first I was going to make use of the diameter. But when I labeled alpha and beta, I realized that I didn’t have to after all. Thanks for bringing the generality of it to my attention as it had not occurred to me.