Step 1: Read the description of the lesion.
An 8 year old boy has a skin lesion on the back that is scaly at the edges and scarred in the centre, meaning the lesion has been slowly spreading outward while healing (and leaving a scar) in the middle.
Step 2: Match this pattern to a diagnosis.
A slowly growing plaque that spreads at the edge while scarring in the middle is a classic description of lupus vulgaris, which is a chronic form of cutaneous tuberculosis caused by Mycobacterium tuberculosis reaching the skin. It typically appears as reddish-brown, soft (apple jelly) nodules that slowly enlarge outward and leave central scarring behind as they heal.
Step 3: Decide the correct investigation.
Because lupus vulgaris is a tissue-level, granulomatous disease, it needs to be confirmed by skin biopsy, which shows caseating (or sometimes non-caseating) epithelioid cell granulomas with Langhans giant cells, and can be paired with acid-fast staining or tuberculosis culture and PCR of the tissue for full confirmation.
Step 4: Rule out the other tests.
Tzanck test is used to look for multinucleated giant cells in vesicular/blistering conditions such as herpes or pemphigus, and gives no information about a granulomatous plaque like this.
KOH mount is used to look for fungal hyphae in suspected fungal skin infections such as tinea (ringworm), which can also show peripheral scaling with some central clearing, but does not show central scarring in the way lupus vulgaris does, and would miss a mycobacterial diagnosis.
Patch test is used to identify the allergen in allergic contact dermatitis and has no role in diagnosing an infectious granulomatous skin lesion.
Final Answer:
The lesion described is lupus vulgaris, and it is best confirmed with a skin biopsy.
\[ \boxed{\text{Skin biopsy}} \]