In the triangle ABC, BC = a, AB + AC = L, make a vertical line from the bisector of the outer angle a 'of the angles B and C, and prove that BD * AE = fixed value with the perpendicular feet of D and E

In the triangle ABC, BC = a, AB + AC = L, make a vertical line from the bisector of the outer angle a 'of the angles B and C, and prove that BD * AE = fixed value with the perpendicular feet of D and E

BD * ce = absin (A / 2) * acsin (A / 2) = AB * ac * (1-cosa) / 2cosa = (a ^ 2-AB ^ 2-ac ^ 2) / (2Ab * AC) so BD * ce = AB * ac * (1-cosa) / 2 = AB * ac * (2Ab * AC-A ^ 2 + AB ^ 2 + AC ^ 2) / (4AB * AC) = [(AB + AC) ^ 2-A ^ 2] / 4 = (1-A ^ 2) / 4

Elden Ring Premiere

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