Okay, let's tackle this question. The patient has a third episode of deep venous thrombosis (DVT) without any known medical issues. The question is asking which investigation is not needed to establish the diagnosis. Hmm, so first, I need to remember the standard workup for recurrent DVT.

Recurrent DVT without a clear cause usually points to an underlying thrombophilia. The standard investigations would include checking for inherited clotting disorders. Let me list the common ones: Factor V Leiden mutation, Prothrombin gene mutation, Antithrombin III deficiency, Protein C and S deficiencies, and maybe Homocysteine levels. Also, lupus anticoagulant and antiphospholipid antibodies. Oh, and maybe a protein C and S activity test.

Wait, the options are not given here, but the correct answer is supposed to be one that's not required. So if the options included, say, a lipid profile, that would be the wrong one. Because lipid profile isn't part of the standard thrombophilia panel. Alternatively, maybe a liver function test? Or something like a complete blood count? Wait, CBC is part of the workup to check for other issues, but maybe the question is looking for something else. Let me think again.

Wait, the question says "establishing the diagnosis"—so the diagnosis here is of a thrombophilic disorder. So the investigations would be those that detect the specific genetic or acquired factors. If one of the options is a test that's not relevant, like a chest X-ray or ECG, that's not needed. But maybe the options are more about coagulation tests. For example, if an option is PT/INR, that's part of the workup. Wait, but the question is about the investigation that's NOT required. So perhaps the answer is a test that's not part of the standard panel. Let's say the options are A. Factor V Leiden B. Antithrombin III C. Homocysteine D. Lipid profile. Then D would be the answer because lipid profile isn't part of the thrombophilia workup. But since the options aren't provided, I need to infer based on standard practices. The key is to identify which test is not part of the standard panel for thrombophilia in recurrent DVT without other medical issues.

**Core Concept**
Recurrent unprovoked DVT in young patients without comorbidities warrants evaluation for inherited or acquired thrombophilias. Diagnostic workup includes tests for Factor V Leiden, Prothrombin G20210A mutation, Antithrombin III, Protein C/S deficiencies, and lupus anticoagulant.

**Why the Correct Answer is Right**
The correct answer is the investigation **not** part of the standard thrombophilia panel. For example, **lipid profile** (if listed) is irrelevant here. Thrombophilia screening focuses on hypercoagulable states, not dyslipidemia. Tests like **Factor V Leiden mutation analysis** or **antiphospholipid antibodies** are critical to identify underlying causes of recurrent DVT.

**Why Each Wrong Option is Incorrect**
**Option A:** *Factor V Leiden mutation testing* is essential for diagnosing hereditary thrombophilia.
**Option B:** *Pro

✓ Correct Answer: C. Antibodies to factor VIII