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Soal 25 besar LMNas UGM SMP

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Diberikan segitiga lancip $ABC$ dengan titik tinggi $H$. Misalkan sinar $AB$ memotong lingkaran luar $BHC$ di $B$ dan $P$; sinar $AC$ memotong lingkaran luar $BHC$ di $C$ dan $Q$.  Diketahui besar $\angle BAC = 60^\circ$. Diketahui pula bahwa panjang $BC=1$. Panjang $PQ$ adalah $\dots$ .

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