Add to ORKGLet ABC be a triangle and let the angle bisector at vertex C intersect the circumcircle at R and the perpendicular bisectors of BC and AC at P and Q, respectively. Let the midpoints of BC and AC be S and T, respectively. Then RQT and RPS have equal areaComponente Curricular::Ensino Médio::MatemáticaComponente Curricular::Educação Superior::Ciências Exatas e da Terra::Matemátic
Let ABC be a triangle. Let AA' and BB' bisect the angles CAB and ABC. Let P be a point on A'B' and P...
Let ABC be a triangle with excenters A', B', and C' opposite A, B, and C, respectively. Let A'', B''...
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 the angle bisector at vertex C intersect the circumcircle at R and the...
Let ABC be a triangle and let A', B', and C' be the contact points of the incircle opposite A, B, an...
Let ABC be a triangle and let A', B', and C' be the contact points of the incircle opposite A, B, an...
Knowledge about plane geometryExtend the angle bisectors of the triangle ABC to meet the circumcircl...
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 with an interior point P. Let AP, BP, and CP intersect BC, AC, and AB at A', B...
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 ABC be a triangle and let the bisectors of the angles at A, B, C meet the opposite sides at A', ...
Let ABC be a triangle. Let AA' and BB' bisect the angles CAB and ABC. Let P be a point on A'B' and P...
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. Let AA' and BB' bisect the angles CAB and ABC. Let P be a point on A'B' and P...
Let ABC be a triangle with excenters A', B', and C' opposite A, B, and C, respectively. Let A'', B''...
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 the angle bisector at vertex C intersect the circumcircle at R and the...
Let ABC be a triangle and let A', B', and C' be the contact points of the incircle opposite A, B, an...
Let ABC be a triangle and let A', B', and C' be the contact points of the incircle opposite A, B, an...
Knowledge about plane geometryExtend the angle bisectors of the triangle ABC to meet the circumcircl...
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 with an interior point P. Let AP, BP, and CP intersect BC, AC, and AB at A', B...
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 ABC be a triangle and let the bisectors of the angles at A, B, C meet the opposite sides at A', ...
Let ABC be a triangle. Let AA' and BB' bisect the angles CAB and ABC. Let P be a point on A'B' and P...
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. Let AA' and BB' bisect the angles CAB and ABC. Let P be a point on A'B' and P...
Let ABC be a triangle with excenters A', B', and C' opposite A, B, and C, respectively. Let A'', B''...
Let I and O be the incenter and circumcenter of a triangle. Let H be the orthocenter of the triangle...