MathDB

Equal angles

Source: VNTST 2024 Problem 5

March 27, 2024

geometrycomplex numberspoles and polarsPascal s theorem

Problem Statement

Let incircle

(I)

of triangle

ABC

touch the sides

BC,CA,AB

at

D,E,F

respectively. Let

(O)

be the circumcircle of

ABC

. Ray

EF

meets

(O)

at

M

. Tangents at

M

and

A

of

(O)

meet at

S

. Tangents at

B

and

C

of

(O)

meet at

T

. Line

TI

meets

OA

at

J

. Prove that

\angle ASJ=\angle IST

.

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