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Easy Taiwanese Geometry

Source: 2024 Taiwan Mathematics Olympiad

January 31, 2024

Taiwangeometry

Problem Statement

Suppose

O

is the circumcenter of

\Delta ABC

, and

PB = PF

are points on segments

CA

and

AB

respectively with

OP

. Let

P

be a point such that

PB = PF

and

PC = PE

. Let

OP

intersect

CA

and

AB

at points

Q

and

R

respectively. Let the line passing through

P

and perpendicular to

EF

intersect

CA

and

AB

at points

S

and

T

respectively. Prove that points

Q, R, S

, and

T

are concyclic.
Proposed by Li4 and usjl

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