Incircle of the Half-Altitude Triangle = Circumcircle of the Mid-Arc Triangle of the Half-Altitude Triangle.

Nine-Point Circle of the Half-Altitude Triangle = Circumcircle of the Euler Triangle of the Half-Altitude Triangle.

Nine-Point Circle of the Half-Altitude Triangle = Circumcircle of the Feuerbach Triangle of the Half-Altitude Triangle.

Brocard Circle of the Half-Altitude Triangle = Circumcircle of the First Brocard Triangle of the Half-Altitude Triangle.

Brocard Circle of the Half-Altitude Triangle = Circumcircle of the Second Brocard Triangle of the Half-Altitude Triangle.

Orthocentroidal Circle of the Half-Altitude Triangle = Circumcircle of the Fourth Brocard Triangle of the Half-Altitude Triangle.

The Incircle of the Half-Altitude Triangle is concentric to the Bevan Circle of the Yff Central Triangle of the Half-Altitude Triangle.

The Nine-Point Circle of the Half-Altitude Triangle is concentric to the Nine-Point Circle of the Fuhrmann Triangle of the Half-Altitude Triangle.

The Spieker Circle of the Half-Altitude Triangle is concentric to the Bevan Circle of the Euler Triangle of the Half-Altitude Triangle.

The Radical Circle of the Excircles of the Half-Altitude Triangle is concentric to the Bevan Circle of the Euler Triangle of the Half-Altitude Triangle.

The Lemoine Circle of the Half-Altitude Triangle is concentric to the Circumcircle of the First Brocard Triangle of the Half-Altitude Triangle.

The Lemoine Circle of the Half-Altitude Triangle is concentric to the Circumcircle of the Second Brocard Triangle of the Half-Altitude Triangle.

The Circumcircle of the Half-Altitude Triangle is congruent to the Bevan Circle of the Euler Triangle of the Half-Altitude Triangle.

The Circumcircle of the Half-Altitude Triangle is congruent to the Bevan Circle of the Feuerbach Triangle of the Half-Altitude Triangle.

The Spieker Circle of the Half-Altitude Triangle is congruent to the Incircle of the Euler Triangle of the Half-Altitude Triangle.

The Spieker Circle of the Half-Altitude Triangle is congruent to the Nine-Point Circle of the Mid-Arc Triangle of the Half-Altitude Triangle.