Constructing Poncelet triangles
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In the diagram above, the two circles are the incircle and circumcircle of the triangle ABC, and so this triangle is an example of a Poncelet polygon. You can click and drag the points A, B and C to change the size and position of these circles.
Since the triangle ABC is a Poncelet polygon, then Poncelet's theorem guarantees that there will be a Poncelet triangle for any initial point X on the outer circle. You can see this from the animation, or you can manually click and drag the point X around the outer circle to verify this.
