Reflection in triangle 2018

03/17/2018 បញ្ចេញមតិ

2018

Let P_0, Q_0, R_0 be points lies on B_0C_0, C_0A_0, A_0B_0.

Let P_k\in [A_0P_0) such that A_0P_0=P_0P_1=...=P_{k-1}P_k and Let A_k\in [P_0A_0) such that P_0A_0=A_0A_1=...=A_{k-1}A_k.

The same ways we get Q_k, B_k and R_k, C_k.

Prove that \displaystyle \frac{[A_kB_kC_k]-[P_kQ_kR_k]}{[A_0B_0C_0]-[P_0Q_0R_0]}=2k+1

Author: Van Khea, Cambodia

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