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

Source: 2017 VWO Flanders MO p2

August 7, 2020

geometrycircumcircleanglesAngle Chasing

Problem Statement

In triangle

\vartriangle ABC

,

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

and

P \ne B

. The point

P

is on the side

[AB]

(with

P \ne A

and

P \ne B

). The inscribed circle of

\vartriangle ABC

intersects the inscribed circle of

\vartriangle ACP

at points

U

and

V

and intersects the inscribed circle of

\vartriangle BCP

at points

X

and

Y

. The rights

UV

and

XY

intersect in

K

. Calculate the

\angle UKX

.

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