Prove that in any triangle the following equivalence relation holds:

**Solution**

We are working on the following shape.

Let be the incenter of the triangle. Thus,

meaning that is tangent to the circumcircle of the triangle . Thus,

(1)

Hence,

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Prove that in any triangle the following equivalence relation holds:

**Solution**

We are working on the following shape.

Let be the incenter of the triangle. Thus,

meaning that is tangent to the circumcircle of the triangle . Thus,

(1)

Hence,