Trouble with angles and lengths

Geometry Level pending

Here,\(\angle ABP=30^{\circ}\) , \(\angle ABQ=67^{\circ}\) , \(\angle BAP=60^{\circ}\) , \(\angle BAQ=46^{\circ}\) , \(\angle PQR=80.6^{\circ}\) , \(AB=200 m \) and \(PR=266.36 m\).\( O \) is the incenter of the triangle \( PQR \) . If \( x \) is the distance of \( O \) from \( RQ \) then we can write \( a<x<a+1 \) . What is the value of \( a\) (in meter) ?

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