The length of the arc of the QR which is formed in a circle from center P will be equal to 9.9 cm.
What will be the Arc?
The arc of the circle is defined as the product of the angle and the radius of the circle.
[tex]Arc=\theta \times r[/tex]
Now it is given in the question that
circle P, i.e. center is point P.
QS is a diameter with a length of 20 cm so radius =10 cm
Given that RP is the radius with
To find the length of arc QR =?
Now for finding the arc of QR we will find the angle [tex]\angle QPR[/tex] since we have the angle [tex]\angle RPS=123^o[/tex].
[tex]\angle QPR+\angle RPS=180[/tex]
[tex]\angle QPR+123=180[/tex]
[tex]\angle QPR=57^o[/tex]
[tex]\angle QPR=\dfrac{57\times\pi}{180} =0.99\ radian[/tex]
Now the formula for finding the arc will be given by
[tex]Arc \ (QR)=\angle QPR\times r[/tex]
[tex]Arc\ (QR)=0.99\times 10=9.9\ cm[/tex]
Thus the length of the arc of the QR which is formed in a circle from center P will be equal to 9.9 cm.
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