**Core Concept**
High-grade liposarcoma is a malignant tumor of adipose tissue that requires prompt and aggressive management to prevent local recurrence and metastasis. Wide local excision is a surgical technique that involves the removal of the tumor along with a margin of normal tissue to ensure complete removal of the cancer.

**Why the Correct Answer is Right**
Wide local excision is the best management option for high-grade liposarcoma because it allows for the removal of the tumor in its entirety while preserving as much normal tissue as possible. This approach is particularly important in the lower extremity, where preserving function and mobility is crucial. The goal of wide local excision is to achieve clear margins, which are essential for preventing local recurrence and improving survival rates. In addition, wide local excision may be combined with adjuvant therapies, such as chemotherapy or radiotherapy, to further reduce the risk of recurrence.

**Why Each Wrong Option is Incorrect**
**Option A:** Amputation of the limb at the mid-thigh is an overly aggressive approach that is typically reserved for cases where the tumor is too large or too advanced to be managed with wide local excision. This approach would result in significant morbidity and loss of function.
**Option C:** Chemotherapy may be used as an adjuvant therapy to treat high-grade liposarcoma, but it is not a primary treatment option. Chemotherapy is typically used in cases where the tumor has recurred or metastasized.
**Option D:** Radiotherapy may also be used as an adjuvant therapy to treat high-grade liposarcoma, but it is not a primary treatment option. Radiotherapy is typically used in cases where the tumor is too large or too advanced to be managed with surgery.

**Clinical Pearl / High-Yield Fact**
The key to managing high-grade liposarcoma is to achieve clear margins through wide local excision. This approach requires careful preoperative planning and intraoperative decision-making to ensure that the tumor is removed completely while preserving as much normal tissue as possible.

✓ Correct Answer: B. Wide local excision