AD H dan o'tadigan aylanaga tangent bo'lib, uning markazi BC ning o'rta nuqtasi bo'lganini isbotlash uchun, agar chiziq aylanaga tangent bo'lsa, u tangentlik nuqtasi radiusiga perpendikulyar bo'lganligini isbotlaymiz. O BC ning o'rta nuqtasi bo'lsin va E AH va markaz O bilan aylaning kesishmasi bo'lsin. O BC ning o'rta nuqtasi bo'lgani uchun DE = DH (chunki ular bir xil aylaning radiuslari). Shuningdek, H orthocenter bo'lgani uchun  BHA = 90 ° -  C. Endi uchburchak AHD ni ko'rib chiqing. Bizda:  AHD = 180 ° -  AHB -  DHA = 180 ° - (90 ° -  C) -  C
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