The Miquel Point
The Miquel point is found when you create a triangle and pick one random point (the green points) on each side of the triangle. Then, you draw a circle for each side going from the vertex to the two random points on the sides adjacent to the vertex. Where the three circles meet is the Miquel point.
To enhance the experience of this worksheet, you can move the points and see how the Miquel point moves around the triangle. You can also move the random points (the green points) located on the lines around and change the sizes of each of the circles.