Question

Чи існує трикутник дві бісектриси якого перпендикулярні

Answer 1

Ответ:

Розглянемо ∆АВС, АО i СО - бісектриси. Нехай ∟AOC = 90°.

Розглянемо ∆АОС - прямокутний, тоді ∟OAC + ∟ОСА = 180° - 90° = 90°.

Позначимо ∟OAC = х, ∟ОСА = у; х + у = 90°, тоді 2х + 2у = 180°.

∟А = 2х

             } властивість бісектриси.

∟С = 2у

В ∆АВС: ∟A + ∟B + ∟C = 180°, а ми маємо ∟А + ∟С = 180°.

Це неможливо, тому не існує трикутник, дві бісектриси якого перпендикулярні.

Объяснение:

Answer 2

Triangle with Perpendicular Bisectors

Yes, a triangle can exist with perpendicular bisectors.

The perpendicular bisectors of a triangle are the lines that pass through the midpoint of each side of the triangle and are perpendicular to those sides. When these bisectors intersect, they do so at a point called the circumcenter, which is equidistant from the three vertices of the triangle.

This means that if the perpendicular bisectors of a triangle are indeed perpendicular to each other, the triangle is referred to as an orthocentric triangle.

The condition for the perpendicular bisectors of a triangle to be perpendicular to each other is that the triangle must be an acute-angled triangle. In obtuse or right-angled triangles, the perpendicular bisectors are not perpendicular to each other.