Pythagoras' theorem

A spider is sitting in the middle of one of the smallest walls in a room and a fly is resting beside the window. What is the shortest distance the spider would have to crawl to catch the fly?

Chris is enjoying a swim but needs to get back for lunch. How far along the bank should she land?

If the hypotenuse (base) length is 100cm and if an extra line splits the base into 36cm and 64cm parts, what were the side lengths for the original right-angled triangle?

A 1 metre cube has one face on the ground and one face against a wall. A 4 metre ladder leans against the wall and just touches the cube. How high is the top of the ladder above the ground?

Which has the greatest area, a circle or a square, inscribed in an isosceles right angle triangle?

A napkin is folded so that a corner coincides with the midpoint of an opposite edge. Investigate the three triangles formed.

An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?

What is the same and what is different about these circle questions? What connections can you make?

Can you make sense of the three methods to work out what fraction of the total area is shaded?

A small circle fits between two touching circles so that all three circles touch each other and have a common tangent? What is the exact radius of the smallest circle?