[/quote]
,
are
can be placed in a 3x3 grid, such that each letter can only be used once, and that 
is not next to 
or 
and 
is not next to 
,
.
be an acute triangle and let 
be the midpoint of 
.
passing through 
and 
and 
at points 
and 
respectively. Let 
be the point such that 
is a parallelogram. Suppose that 
.
be a circle with centre 
,
a convex quadrilateral such that each of the segments 
and 
is tangent to 
be the circumcircle of the triangle 
.
beyond 
meets 
,
beyond 
meets 
.
and 
beyond 
meet 
and ![\[A D+D T+T X+X A=C D+D Y+Y Z+Z C.\]](http://latex.artofproblemsolving.com/8/2/6/8261276053071cc6cc06dda824a883426bf1d4ac.png)
,
be the intersection point of segments 
.
are 
is the center of the square. Prove that points 
,![\[ \textbf{(A)}\ 24 \qquad
\textbf{(B)}\ 30 \qquad
\textbf{(C)}\ 46 \qquad
\textbf{(D)}\ 66 \qquad
\textbf{(E)}\ 74
\]](http://latex.artofproblemsolving.com/8/2/f/82ffc15072ca99f6cd1abc312781eb4827817356.png)
be a scalene triangle, 
its medial triangle, and 
)
).
be the circumcevian triangle of 
be the pedal triangle of 
be the reflection in 
.
,
cyclically.
be the reflection in 
of 
,
cyclically.
be the reflection in 
of 
,
cyclically.
,
,
and the orthocentroidal circle of 
again at 
is a trapezium.
has 
.
intersects 
intersects 
at 
.
,
be the midpoints of arcs 
,
passes through the feet of the perpendiculars from 
and 
.
passes through the feet of the perpendiculars from 
and 
are similar to each other.
again at 
cuts 
lie on 
.
at 
respectively. Let circumcircle of 
cuts 
.
.
in circumcircle of 
.
.
.
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this is my 100th post! i cant believe it. 
P.S. can everyone who reads this give it an upvote? thx!
P.S. can everyone who reads this give it an upvote? thx!
This post has been edited 1 time. Last edited by JohannIsBach, Mar 10, 2025, 4:08 PM
more posts to get to 1000!
more 2 go
