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MathNet 2007-part-03 — 185 problems (EN–VI) Question 72

Math Olympiad Vault · MathNet 2007-part-03 — 185 problems (EN–VI)

Question 72

A circle inscribed in a square,
Has two chords as shown in a pair.
It has radius $2$,
And $P$ bisects $TU$.
The chords' intersection is where?

Question illustration

Answer the question by giving the distance of the point of intersection from the center of the circle.