The problem at hand concerns the application of the "II Lagrange's formula". Would you like to try solving it?

Liudmyla Hetmanenko @Liudmyla-Hetmanenko

13 June 2024 1 8K Report

In triangle ABC, the bisector AL₁ is drawn.

Points O₁, O₂, O are the centers of the circles circumscribed around triangles ACL₁, ABL₁, ABC, respectively.

The radii are denoted as R₁, R₂, R for the respective circles.

The task is to find OO₁ and OO₂.

Given: ∠CAL₁ = ∠BAL₁; γ₁ (O₁; R₁ = O₁ A); γ₂ (O₂; R₂ = O₂ A); γ₀ (O; R = OA).

Find: OO₁, OO₂

Steftcho P. Dokov

Apparently, both share same length OO1 = OO2 = sqrt(R*R - R1*R2)

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