Approach via vessel size classification:
Vasculitides are classified by vessel size. The clinical scenario -- weak upper limb pulses + low BP + retinal haemorrhages in a 12-year-old -- localises pathology to large vessels (aorta and branches).
Among the options:
- $\text{PAN}$: medium-vessel vasculitis, no pulse deficits
- Microscopic polyangiitis: small-vessel, causes renal and pulmonary disease
- HSP: small-vessel IgA vasculitis in children (purpura, joints, gut, kidney)
- Takayasu arteritis: large-vessel granulomatous vasculitis affecting the aorta and its branches
Takayasu arteritis causes progressive stenosis of the subclavian arteries leading to absent/weak upper limb pulses. The retinal haemorrhages are due to occlusive retinopathy from reduced carotid blood flow. It predominantly affects young females and children.
\[\boxed{\text{Takayasu arteritis}}\]