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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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