ABSTRACT
No matter what the position of X and Y, the https://www.w3.org/1998/Math/MathML"> ∠ Y X B https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003341468/d4c0c4c8-8291-444b-87ca-3efd613fe6ea/content/math3_1.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> and https://www.w3.org/1998/Math/MathML"> ∠ X Y B https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003341468/d4c0c4c8-8291-444b-87ca-3efd613fe6ea/content/math3_2.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> are always the same size, because angles on the same chord of a circle are equal. Thus the triangle BXY is always similar to the triangle https://www.w3.org/1998/Math/MathML"> B X ′ Y ′ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003341468/d4c0c4c8-8291-444b-87ca-3efd613fe6ea/content/math3_3.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> .
