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'Incircles' printed from https://nrich.maths.org/
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.