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 for a solution.