# Triangle Projection Problem

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 BP is on C1PA 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 for a solution.

## 3 thoughts on “Triangle Projection Problem”

1. Jim Stevenson Post author

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(Update 12/31/2022) I finally figured out a way to remove the bold face.

2. Oscar Rojas

No equations needed, just observations:

On C1, by inscribed angle theorem, measure of angle APB is constant, no matter the position of P.

On C2, by converse of outside angle theorem, measure of arc A’B’ is constant, as well as the length of chord A’B’.