On the Locus of a Pedal Point of a Quadrilateral Such That Opposite Sides of the Pedal Quadrilateral Form a Constant Angle

The article deals with a problem related to plane quadrilaterals, which is connected with the well‐known Wallace–Simson theorem. If K , L , M , N are the feet of perpendiculars from a point P to the sides of a quadrilateral, then the locus of P such that lines K N and L M form a constant angle is generally a circle. It turns out that the proof based on finding the equation of the locus of P is quite complex, time‐consuming, and requires human intervention in addition to a computer. Therefore, we decided to present a classical geometric proof using the Miquel point of a quadrilateral. Furthermore, the properties of a cyclic quadrilateral are studied in a similar way to the properties of a triangle in the Wallace–Simson theorem.