2024 IMO Problems/Problem 4
Let be a triangle with
. Let the incentre and incircle of triangle
be
and
, respectively. Let
be the point on line
different from
such that the line
through
parallel to
is tangent to
. Similarly, let
be the point on line
different from
such that the line through
parallel to
is tangent to
. Let
intersect the circumcircle of
triangle
again at
. Let
and
be the midpoints of
and
, respectively.
Prove that
.
Video Solution
Video Solution
Part 1: Derive tangent values and
with trig values of angles
,
,
https://youtu.be/p_AmooMMln4
Part 2: Derive tangent values and
with side lengths
,
,
, where
is the midpoint of
Part 3: Prove that and
.
~Steven Chen (Professor Chen Education Palace, www.professorchenedu.com)