Given a square ABCD of sides 10 cm, and using the corners as
centres, construct four quadrants with radius 10 cm each inside the
square. The four arcs intersect at P, Q, R and S. Find the area
enclosed by PQRS.
Age 14 to 16 Challenge Level:
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.
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.