Δευτέρα, 9 Απριλίου 2018

Ίσες ακτίνες

The given circles $ω_1$ and $ω_2$ lie inside an angle of vertex $O$, touching the arms. A ray drawn from point $O$ intersects circle $ω_1$ at points $A_1$ and $B_1$, and circle $ω_2$ at points $A_2$ and $B_2$, such that $OA_1<OB_1<OA_2<OB_2$. 
Circle $γ_1$ touches the circle $ω_1$ on the inside, and also touches the tangents drawn to circle $ω_2$ from point $A_1$. Similarly, circle $γ_2$ touches the circle $ω_2$ on the inside, and also touches the tangents drawn to circle $ω_1$ from point $B_2$. Prove that the radii of the circles $γ_1$ and $γ_2$ are equal.
KöMaL Problems in Mathematics

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