MathDB

Nice collinearity

Source: Kvant Magazine No. 9 2022 M2717

March 8, 2023

Kvantgeometry

Problem Statement

In an acute triangle

ABC

the heights

AD, BE

and

CF

intersecting at

H{}

. Let

O{}

be the circumcenter of the triangle

ABC

. The tangents to the circle

(ABC)

drawn at

B{}

and

C{}

intersect at

T{}

. Let

K{}

and

L{}

be symmetric to

O{}

with respect to

AB

and

AC

respectively. The circles

(DFK)

and

(DEL)

intersect at a point

P{}

different from

D{}

. Prove that

P, D

and

T{}

lie on the same line.
Proposed by Don Luu (Vietnam)

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