This is a Maths Item of the Month (MIOM) problem that seems opaque at first. (“The Maths Item of the Month is a monthly problem aimed at teachers and students of GCSE and A level Mathematics.”)

“Two fixed circles, *C*_{1} and *C*_{2}, intersect at *A* and *B*. *P* is on *C*_{1}. *PA* and *PB* produced meet *C*_{2} at *A’* and *B’* respectively. How does the length of the chord *A’B’* change as *P* moves?”

Just start noticing relationships and the answer falls out nicely.

(MIOM problems often appear on MathsMonday and are also produced by Mathematics Education Innovation (MEI).)

See the Triangle Projection Problem