[Trigonometric ratios in a right triangle]
[Trigonometric equations

Isosceles triangles $ABC (AB = BC)$ and $A_{1}B_{1}C_{1} \quad (A_{1}B_{1} = B_{1}C_{1})$ are similar, and $BC: B_{1}C_{1} = 4: 3$.

Vertex $B_{1}$ is located on side $AC$, vertices $A_{1}$ and $C_{1}$ are on the extensions of side $BA$ beyond point $A$ and side $CB$ beyond point $B$, respectively, and $A_{1}C_{1} \perp BC$. Find the angle $B$.

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See problems $\underline{53823}$ and $\underline{53824}$.

## Answer

$2 \arccos 2 / 3$.