Add to ORKGLet ABC be a triangle and let A', B', and C' be the midpoints of BC, AC, and AB, respectively. Let A'', B'', and C'' be the centers of the nine-point circles of the triangles AB'C', BC'A', and CA'B', respectively. Then A''B''C'' is homothetic with ABC in the ratio 1:2. In the figure s(XY) is the slope of XYComponente Curricular::Ensino Médio::MatemáticaComponente Curricular::Educação Superior::Ciências Exatas e da Terra::Matemátic
Let I and O be the incenter and circumcenter of a triangle. Let H be the orthocenter of the triangle...
Let ABC be a triangle. Let A'A'', B'B'', and C'C'' be tangents to the incircle of ABC and parallel t...
Let I and O be the incenter and circumcenter of a triangle. Let H be the orthocenter of the triangle...
Let ABC be a triangle and let A', B', and C' be the midpoints of BC, AC, and AB, respectively. Let A...
Let ABC be a triangle. Let A', B', and C' be points on BC, AC, and AB, respectively. Let A'', B'', a...
Let ABC be a triangle with an interior point P. Let AP, BP, and CP intersect BC, AC, and AB at A', B...
Let ABC be a triangle with nine-point center N. Let B' be the foot of the altitude from B. Let the c...
Let ABC be a triangle with nine-point center N. Let B' be the foot of the altitude from B. Let the c...
If ABC is a triangle with side lengths a, b, and c, altitudes α, β, and γ, and circumradius R, then...
If ABC is a triangle with side lengths a, b, and c, altitudes α, β, and γ, and circumradius R, then...
Let ABC be a triangle and let A', B', and C' be symmetric to P with respect to the midpoints of BC, ...
Let ABC be a triangle. Let the feet of the altitudes from A, B, and C be A', B' and C', respectively...
Let ABC be a triangle and P be an arbitrary point. Let A', B', and C' be symmetric to P with respect...
Let ABC be a triangle and let P be a point. Then the circumcircles of the medial triangles of ABC, P...
Let ABC be a triangle and let P be a point. Then the circumcircles of the medial triangles of ABC, P...
Let I and O be the incenter and circumcenter of a triangle. Let H be the orthocenter of the triangle...
Let ABC be a triangle. Let A'A'', B'B'', and C'C'' be tangents to the incircle of ABC and parallel t...
Let I and O be the incenter and circumcenter of a triangle. Let H be the orthocenter of the triangle...
Let ABC be a triangle and let A', B', and C' be the midpoints of BC, AC, and AB, respectively. Let A...
Let ABC be a triangle. Let A', B', and C' be points on BC, AC, and AB, respectively. Let A'', B'', a...
Let ABC be a triangle with an interior point P. Let AP, BP, and CP intersect BC, AC, and AB at A', B...
Let ABC be a triangle with nine-point center N. Let B' be the foot of the altitude from B. Let the c...
Let ABC be a triangle with nine-point center N. Let B' be the foot of the altitude from B. Let the c...
If ABC is a triangle with side lengths a, b, and c, altitudes α, β, and γ, and circumradius R, then...
If ABC is a triangle with side lengths a, b, and c, altitudes α, β, and γ, and circumradius R, then...
Let ABC be a triangle and let A', B', and C' be symmetric to P with respect to the midpoints of BC, ...
Let ABC be a triangle. Let the feet of the altitudes from A, B, and C be A', B' and C', respectively...
Let ABC be a triangle and P be an arbitrary point. Let A', B', and C' be symmetric to P with respect...
Let ABC be a triangle and let P be a point. Then the circumcircles of the medial triangles of ABC, P...
Let ABC be a triangle and let P be a point. Then the circumcircles of the medial triangles of ABC, P...
Let I and O be the incenter and circumcenter of a triangle. Let H be the orthocenter of the triangle...
Let ABC be a triangle. Let A'A'', B'B'', and C'C'' be tangents to the incircle of ABC and parallel t...
Let I and O be the incenter and circumcenter of a triangle. Let H be the orthocenter of the triangle...