Inspired my myself!

Geometry Level 3

A particle is on the point \((3,5)\) on the plane. It goes 10 units in the direction of positive \(x\)-axis. Then it turns towards right making an angle of 90 degrees with its initial direction and goes ahead 5 units, Now it again takes a right turn and goes ahead 2.5 units. It keeps turning right and travels half the distance traveled in the turn just before it . This goes on without end. Find the final distance of the particle from the origin \( (0,0) \)?

The answer would come in the form square root of \(x\), submit your answer as \(x\).

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