Perimeter 83352

A circle with a diameter of 30 cm is cut by a chord t = 16 cm.
Calculate the perimeter and area of the smaller segment.

Correct answer:

o1 =  32.8761 cm
S1 =  25.062 cm2

Step-by-step explanation:

D=30 cm t=16 cm  r=D/2=30/2=15 cm  sin α/2 = t/2 : r  A=2 arcsin(rt/2)=2 arcsin(1516/2)1.1251 rad  α=A  °=A π180   °=1.1251 π180   °=64.46191  °  o=π D=3.1416 3094.2478 cm K=360α=36064.46190.1791  o1=K o+t=0.1791 94.2478+16=32.8761 cm
h2 + (t/2)2 = r2  h=r2(t/2)2=152(16/2)2=161 cm12.6886 cm v=rh=1512.68862.3114 cm  S2=K π r2=0.1791 3.1416 152126.5707 cm2  S3=2t h=216 12.6886=8 161 cm2101.5086 cm2  S1=S2S3=126.5707101.5086=25.062 cm2



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