2

Part of 2017 Flanders Math Olympiad

Problems(1)

angle chasing, 3 circumcircles, starting with a 50-60-70 triangle

Source: 2017 VWO Flanders MO p2

\vartriangle ABC

\angle A = 50^o, \angle B = 60^o

\angle C = 70^o

P

[AB]

P \ne A

P \ne B

). The inscribed circle of

\vartriangle ABC

intersects the inscribed circle of

\vartriangle ACP

U

V

and intersects the inscribed circle of

\vartriangle BCP

X

Y

UV

XY

K

. Calculate the

\angle UKX

geometrycircumcircleanglesAngle Chasing