# 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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