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, C1 and C2, intersect at A and B. P is on C1. PA and PB produced meet C2 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