If $H$ is the orthocenter of acute triangle $ABC$, then the circumcenters of triangles $ABH$, $BCH$, $CAH$ determine a triangle congruent to $ABC$
89493
Prove that circumcentre of $ABH,BCH,CAH$ are the vertices of a triangle congruent to $ABC$
110672
Is it true that $aH = bH$ iff $ab^{-1} \in H$
73799
In a convex Quadrilateral ABCD, $\measuredangle ABC = \measuredangle BCD = 120^{\circ}$.Prove that: $ AC + BD \ge AB + BC + CD$
96095
If $\{a_1,\dots,a_{\phi(n)}\}$ is a reduced residue system, what is $a_1\cdots a_{\phi(n)}$ congruent to?
96065
Question about sines of angles in an acute triangle
118716
If $ABCD$ is a cyclic quadrilateral, then $AC\cdot(AB\cdot BC+CD\cdot DA)=BD\cdot (DA\cdot AB+BC\cdot CD)$
111003
Prove that if $A\triangle B = C\triangle B$, then $A = C$
35438
Ordering $n$ points in $\Bbb{R}^d$ so that every three consecutive points determine an acute angle
100404
Angle subtended at the centre by a segment of a circle
216
In a $\triangle ABC,a^2+b^2+c^2=ac+ab\sqrt3$,then the triangle is
50417
Prove that the triangles $ABC$ and $AB^{'}C^{'}$ have the same incentre.
112740
Prove the triangle is equilateral given that a quadrilateral related to its circumcircle is a kite
47342
Figure out if a fourth point resides within an angle created by three other points
127866
Two triangles and their content ratio
70402
Geometry Triangle Question 3
45702
For any triangle with sides $a$, $b$, $c$, show that $a^2b(a-b)+b^2c(b-c)+c^2a(c-a)\ge 0$
52642
Show that $\text{C}/c \cong (c/(\text{C}^{\text{op}}))^{\text{op}}$