2

Part of 2000 Czech and Slovak Match

Problems(1)

incircle, circumcircles and 3 orthogonal circles

Source: Czech and Slovak Match 2000 P2

{ABC}

{k}

its incircle and

{k_a,k_b,k_c}

three circles orthogonal to

{k}

passing through

{B}

{C, A}

{C}

{A}

{B}

respectively. The circles

{k_a,k_b}

{C'}

; in the same way we obtain the points

{B'}

{A'}

. Prove that the radius of the circumcircle of

{A'B'C'}

is half the radius of

{k}

geometryorthogonal circlescircumcircle