**Core Concept**
Hemophilia A is a genetic disorder caused by a deficiency or dysfunction of a specific protein essential for blood clotting. This protein, known as factor VIII, plays a crucial role in the intrinsic pathway of blood coagulation.

**Why the Correct Answer is Right**
The correct answer is related to the pathophysiology of hemophilia A. Factor VIII is a critical component of the intrinsic pathway, which is activated when blood comes into contact with a foreign surface. It works in conjunction with other factors, such as factor IX and factor X, to form a complex that activates factor X to its active form, leading to the formation of a blood clot. Without sufficient factor VIII, the blood clotting process is severely impaired, resulting in prolonged bleeding.

**Why Each Wrong Option is Incorrect**
* **Option A:** This option is incorrect because the primary issue in hemophilia A is not related to factor IX, but rather to factor VIII. While factor IX is also involved in the intrinsic pathway, its deficiency leads to hemophilia B, not hemophilia A.
* **Option B:** This option is incorrect because the primary issue in hemophilia A is not related to a problem with platelet function. Platelets are responsible for initiating the blood clotting process, but they are not directly affected in hemophilia A.
* **Option C:** This option is incorrect because the primary issue in hemophilia A is not related to a problem with the vascular system. The vascular system is responsible for transporting blood throughout the body, but it is not directly affected in hemophilia A.

**Clinical Pearl / High-Yield Fact**
A key clinical feature of hemophilia A is the presence of joint bleeds, which can lead to chronic joint inflammation and degeneration if left untreated. This is because the blood clotting process is impaired, leading to prolonged bleeding into the joint space.

**Correct Answer: C. Problem with intrinsic pathway of blood coagulation**