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Non-homogenous Inequality
Adywastaken 0
Source: NMTC 2024/7
such that 
. Show that 
. When will equality hold?
0 replies
Classic Diophantine
Adywastaken 0
Source: NMTC 2024/6
Find all natural number solutions to 
.
.
0 replies
Indian Geo
Adywastaken 0
Source: NMTC 2024/5
has 
obtuse. Let 
, 
, 
be the feet of the altitudes from 
, 
, 
respectively. Let 
, 
, 
be arbitrary points on 
, 
, 
respectively. The circles with diameter 
, 
, 
are drawn. Show that the lengths of the tangents from the orthocentre of 
to these circles are equal.
0 replies
Interesting inequalities
sqing 2
N
by sqing
Source: Own
Let 
Prove that
Where 
Let
Prove that
Let 
Prove that
Let 
Prove that
Prove that
Where 
Let
Prove that
Let 
Prove that
Let 
Prove that
2 replies
such that 
.
Angle ratio
Adywastaken 0
Source: NMTC Junior 2024/4
An acute angle triangle 
is inscribed in a circle. Given 
and 
. Let 
and 
be the orthocentre and incentre of respectively. Find the ratio of 
to 
.
is inscribed in a circle. Given 
and 
. Let 
and 
be the orthocentre and incentre of respectively. Find the ratio of 
to 
.
0 replies
concyclic , touchpoints of incircle related
parmenides51 2
N
by Blackbeam999
Source: All-Russian MO 1994 Regional (R4) 11.3
A circle with center 
is tangent to the sides 
, 
, 
of a triangle 
at points 
respectively. The lines 
and 
meet 
at points 
and 
. Prove that the circumcircle of triangle 
and points and 
lie on a line.
is tangent to the sides , , 
of a triangle at points 
respectively. The lines 
and 
meet 
at points 
and 
. Prove that the circumcircle of triangle 
and points and lie on a line.
2 replies
8 degree polynomial
Adywastaken 0
Source: NMTC Junior 2024/3
Let 
such that the polynomial 
has 8 linear factors of the form 
with 
for 
. Find all possible values of the constant 
.
such that the polynomial 
has 8 linear factors of the form 
with 
for 
. Find all possible values of the constant 
.
0 replies
