3 citations · 3 across the 11 of their papers we have counts for
11 papers · 1 filter
Eight circles through the Orthocentre
Christopher Bradley
A construction is given of five Hagge circles complete with supporting calculations.
A Construction to find any Circle through a Given Point
Christopher Bradley
A construction similar to Hagge's construction for circles through the orthocentre is shown to apply for any point.
Miquel circles and Cevian lines
Christopher Bradley
Two theorems are presented concerning the Miquel point configuration, when the operative points on the sides of the triangle are the feet of Cevians,
A Singular Miquel Configuration and the Miquel Direct Similarity
Christopher Bradley
Let ABC be a triangle with P on AB, and let circle APC meet BC at Q and circle BPC meet CA at R, then the special Miquel configuration is when P, Q, R are the operative points on t…
Generalization of the Wallace-Simson line
Christopher Bradley
A Wallace-Simson line of a point J has the property that it passes through the midpoint Q of HJ, where H is the orthocentre. By allowing Q to move on the perpendicular bisector of…
On The Ten Point Wood-Desargues' Configuration
Christopher Bradley
The ten pairs of directly similar triangles in perspective in the Wood-Desargues' configuration have ten common Hagge circle centres. These centres are known to lie one each of the…
Generalizations of Hagge's Theorems
Christopher J Bradley
Two generalizations of Hagge's theorems are described. In the first we consider what happens when one moves from the orthocentre to a general point. What one loses by doing so is t…
The Four Hagge Circles
Christopher J Bradley
The four Hagge circles of the triangles BCD, ACD, ABD, ABC of a cyclic quadrilateral ABCD with respect to an appropriate common axis of inverse similarity share many features which…
The Story of Hagge and Speckman
Christopher J Bradley
This concerns theory first developed by Hagge and Speckman in the Edwardian era. Speckman investigated triangles that were simultaneously in perspective and indirectly similar. On…
Omega Circles
Christopher J Bradley
Circles through the Brocard points (Omega circles) share nearly all the properties of circles through the orthocentre including the fact that key triangles inscribed in them are in…
Studies in Similarity
Christopher J Bradley
Three circles define each of the Brocard points of a triangle. If one adds the three circles through a pair of vertices and the orthocentre one has nine circles. It is described ho…