if ray AS bisects ∠CAB and ray BT bisects ∠ABC and m∠APS = 180 and m∠BPT = 180 and PZ ⊥ ZA and PX ⊥ XA and PX ⊥ XB and PY ⊥ YB and PZ ⊥ ZC and PY ⊥ YC, then ray CP bisects ∠BCA

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