apply4good wrote:

It is easy.

arcPO=arcQR=anglePEO*2/360*circumference=35*2/360*18pi=70/360*18pi=70/20pi

arcOR=Half of circumference=1/2*18pi=9pi

arcPQ=arcOR-2*arcPO=9pi-70/20pi*2=9pi-7pi=2pi

The original question asks for length of line segment PQ and not the arc. I guess the question meant the opposite.

There is an easier way to find the length of an arc i.e. (theta/360)*2*Pi*r where theta is the angle the arc forms at the center. In this case segment PCQ where c is the center of the circle subtends a angle of 40deg at the center of the circle. Applying it to the above formula, length of the arc is (40/360)*2*pi*9 = 2pi

Calculation of angle PCQ

PC=CR hence CPR=CRP=35deg

PQ ll OR hence QPR=PRO=35 deg

CP = CQ hence CPQ(CPR+RPQ) = PQC=70deg

PEQ = 180-CPQ-PQC = 40deg

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