How do i answer this question? PR is the diameter of circle O If the measure of arc QR =50 degrees then the measure of arc QS=?  

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jeew-m | College Teacher | (Level 1) Educator Emeritus

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It is given that arc QR = 50

`S = Rtheta `


S = arc length

R = radius of arc

`theta` = angle generated by arc at the center


`arc QR = ORxxangleQOR`


Consider the triangles QOT and SOT.

According to the figure both are right triangles.

Hypotenuse of both QOT and SOT triangles is the radius of the circle. Further leg OT is common for both triangles. Therefore QOT and SOT triangles are equilateral.

So we can say;

`angleSOT = angleQOT`

`angleSOR = angleQOR`


Length of arc RS `= ORxxSOR = ORxxQOR = 50`


So arc length QS `= QR+RS = 50+50 = 100`


So the arc length of QS is 100.



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