A semicircle with three tangents. The tangency points are shown. Prove that the red line segments are concurrent.

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## Solution

Both the intersection point of red diagonals and the tangent point on the circle have the same horizontal distance to the perpendicular tangent on the left. Hence a perpendicular line from tangent point to the diameter goes through the intersection point.

## Poem

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Famous argument

Spoken by the oppressed people

A warning for the enemy

To stop the dictators

And prevent death

To avoid civil suffering

Two words

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