M is any point on the line AB. Squares of side length AM and MB are
constructed and their circumcircles intersect at P (and M). Prove
that the lines AD and BE produced pass through P.
Three Four Five
Stage: 4 Challenge Level:
As shown in the diagram, two semi-circles (each of radius $1/2$)
touch each other, and a semi-circle of radius 1 touches both of
them. Find the radius of the circle which touches all three
semi-circles, and find a 3-4-5 triangle in the diagram.
The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the
NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to
embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities
can be found here.