**Core Concept**
The girl's presentation suggests a bleeding disorder, specifically an issue with the intrinsic pathway of coagulation. The prolonged activated partial thromboplastin time (APTT) indicates a problem with the intrinsic pathway, which involves factors VIII, IX, XI, and XII, as well as the contact activation system.

**Why the Correct Answer is Right**
The most likely diagnosis is Hemophilia A (also known as Classic Hemophilia), which is caused by a deficiency or dysfunction of factor VIII. This leads to a failure in the intrinsic pathway, resulting in prolonged APTT and recurrent joint bleeding due to the accumulation of blood products in the joints. The normal prothrombin time (PT) suggests that the extrinsic pathway is intact, ruling out other bleeding disorders such as hemophilia B (factor IX deficiency) or severe combined deficiency of factors V and VIII.

**Why Each Wrong Option is Incorrect**
* **Option A:** This is incorrect because Hemophilia B, caused by factor IX deficiency, typically presents with a normal APTT and a prolonged PT, which is not consistent with the provided lab results.
* **Option B:** This is incorrect because Hemophilia A is the most common inherited bleeding disorder, and the provided lab results are consistent with this diagnosis. Factor XI deficiency is rare and typically presents with a mild bleeding tendency.
* **Option C:** This is incorrect because von Willebrand disease typically presents with a prolonged APTT and a prolonged PT, as well as a low von Willebrand factor level, which is not mentioned in the scenario.
* **Option D:** This is incorrect because Factor XII deficiency typically presents with a prolonged APTT, but the bleeding tendency is usually mild and not as severe as in Hemophilia A.

**Clinical Pearl / High-Yield Fact**
Hemophilia A is an X-linked recessive disorder, meaning it primarily affects males. However, females can be carriers and may exhibit mild symptoms due to lyonization (X-chromosome inactivation), which can lead to variable expression of the disease.

**Correct Answer:** A. Hemophilia A.