Why do this problem?

The first two parts require only applying the idea that the tangents from an external point to a circle are equal and the radius is perpendicular to the tangent at the point of contact.

Possible approach

The first two parts could be tackled by the learners independently.

For the third part the formula for generating Pythagorean triples is needed.

Key questions

What facts do you know about tangents to circles?

What do you know about areas of triangles?

What is the formula for generating Pythagorean triples?

Possible support

Three articles: Pythagorean Triples I, Pythagorean Triples II and Picturing Pythagorean Triples.

Possible extension

The problem Pythagoras Mod 5

See the article Incircles which generalises this problem.