Let AH_{A}, BH_{B},
CH_{C}
be the altitudes of a triangle ABC. The extensions of AH_{A}, BH_{B},
CH_{C}
intersect the circumcircle O at A_{1}, B_{1}, C_{1}.
Prove that (1) H_{A}H_{B} // A_{1}B_{1},
similarly H_{B}H_{C} // B_{1}C_{1}, H_{A}H_{C} // A_{1}C_{1};
(2) Area A_{1}, B_{1}C_{1}.

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Ten problems: 1411-1420

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