Incircle of the Fourth Brocard Triangle = Circumcircle of the Mid-Arc Triangle of the Fourth Brocard Triangle.

Circumcircle of the Fourth Brocard Triangle = Orthocentroidal Circle.

Nine-Point Circle of the Fourth Brocard Triangle = Circumcircle of the Euler Triangle of the Fourth Brocard Triangle.

Nine-Point Circle of the Fourth Brocard Triangle = Circumcircle of the Feuerbach Triangle of the Fourth Brocard Triangle.

Brocard Circle of the Fourth Brocard Triangle = Circumcircle of the First Brocard Triangle of the Fourth Brocard Triangle.

Brocard Circle of the Fourth Brocard Triangle = Circumcircle of the Second Brocard Triangle of the Fourth Brocard Triangle.

Orthocentroidal Circle of the Fourth Brocard Triangle = Circumcircle of the Fourth Brocard Triangle of the Fourth Brocard Triangle.

The Incircle of the Fourth Brocard Triangle is concentric to the Bevan Circle of the Yff Central Triangle of the Fourth Brocard Triangle.

The Nine-Point Circle of the Fourth Brocard Triangle is concentric to the Nine-Point Circle of the Fuhrmann Triangle of the Fourth Brocard Triangle.

The Spieker Circle of the Fourth Brocard Triangle is concentric to the Radical Circle of the Excircles of the Fourth Brocard Triangle.

The Spieker Circle of the Fourth Brocard Triangle is concentric to the Bevan Circle of the Euler Triangle of the Fourth Brocard Triangle.

The Radical Circle of the Excircles of the Fourth Brocard Triangle is concentric to the Spieker Circle of the Fourth Brocard Triangle.

The Radical Circle of the Excircles of the Fourth Brocard Triangle is concentric to the Bevan Circle of the Euler Triangle of the Fourth Brocard Triangle.

The Brocard Circle of the Fourth Brocard Triangle is concentric to the Lemoine Circle of the Fourth Brocard Triangle.

The Lemoine Circle of the Fourth Brocard Triangle is concentric to the Brocard Circle of the Fourth Brocard Triangle.

The Lemoine Circle of the Fourth Brocard Triangle is concentric to the Circumcircle of the First Brocard Triangle of the Fourth Brocard Triangle.

The Lemoine Circle of the Fourth Brocard Triangle is concentric to the Circumcircle of the Second Brocard Triangle of the Fourth Brocard Triangle.

The Incircle of the Fourth Brocard Triangle is congruent to the Spieker Circle of the Fourth Brocard Triangle of the Anticomplementary Triangle.

The Circumcircle of the Fourth Brocard Triangle is congruent to the Bevan Circle of the Fourth Brocard Triangle of the Medial Triangle.

The Circumcircle of the Fourth Brocard Triangle is congruent to the Orthocentroidal Circle of the Euler Triangle of the Anticomplementary Triangle.

The Circumcircle of the Fourth Brocard Triangle is congruent to the Nine-Point Circle of the Fourth Brocard Triangle of the Anticomplementary Triangle.

The Circumcircle of the Fourth Brocard Triangle is congruent to the Bevan Circle of the Fourth Brocard Triangle of the Euler Triangle.

The Circumcircle of the Fourth Brocard Triangle is congruent to the Bevan Circle of the Euler Triangle of the Fourth Brocard Triangle.

The Circumcircle of the Fourth Brocard Triangle is congruent to the Bevan Circle of the Feuerbach Triangle of the Fourth Brocard Triangle.

The Nine-Point Circle of the Fourth Brocard Triangle is congruent to the Orthocentroidal Circle of the Medial Triangle.

The Nine-Point Circle of the Fourth Brocard Triangle is congruent to the Orthocentroidal Circle of the Euler Triangle.

The Nine-Point Circle of the Fourth Brocard Triangle is congruent to the Circumcircle of the Fourth Brocard Triangle of the Medial Triangle.

The Nine-Point Circle of the Fourth Brocard Triangle is congruent to the Circumcircle of the Fourth Brocard Triangle of the Euler Triangle.

The Spieker Circle of the Fourth Brocard Triangle is congruent to the Incircle of the Fourth Brocard Triangle of the Medial Triangle.

The Spieker Circle of the Fourth Brocard Triangle is congruent to the Incircle of the Fourth Brocard Triangle of the Euler Triangle.

The Spieker Circle of the Fourth Brocard Triangle is congruent to the Incircle of the Euler Triangle of the Fourth Brocard Triangle.

The Spieker Circle of the Fourth Brocard Triangle is congruent to the Nine-Point Circle of the Mid-Arc Triangle of the Fourth Brocard Triangle.

The Bevan Circle of the Fourth Brocard Triangle is congruent to the Orthocentroidal Circle of the Anticomplementary Triangle.

The Bevan Circle of the Fourth Brocard Triangle is congruent to the Circumcircle of the Fourth Brocard Triangle of the Anticomplementary Triangle.

The Brocard Circle of the Fourth Brocard Triangle is congruent to the Orthocentroidal Circle of the First Brocard Triangle.

The Brocard Circle of the Fourth Brocard Triangle is congruent to the Circumcircle of the Fourth Brocard Triangle of the First Brocard Triangle.

The Orthocentroidal Circle of the Fourth Brocard Triangle is congruent to the Circumcircle of the Fourth Brocard Triangle of the Circum-Medial Triangle.