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Geometry Mathley 12.3 concurency

Source:

June 7, 2020

geometryconcurrentcircumcircleTangents

Problem Statement

Points

E,F

are chosen on the sides

CA,AB

of triangle

ABC

. Let

(K)

be the circumcircle of triangle

AEF

. The tangents at

E, F

of

(K)

intersect at

T

. Prove that (a)

T

is on

BC

if and only if

BE

meets

CF

at a point on the circle

(K)

, (b)

EF, PQ,BC

are concurrent given that

BE

meets

FT

at

M, CF

meets

ET

at

N, AM

and

AN

intersects

(K)

at

P,Q

distinct from

A

.
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