Common chord

The common chord of the two circles c1 and c2 is 3.8 cm long. This chord forms an angle of 47° with the radius r1 of the circle c1 and an angle of 24° 30´ with the radius r2 of the circle c2. Calculate both radii and the distance between the two centers of the circles.

Correct answer:

r1 =  2.7859 cm
r2 =  2.088 cm
x =  2.9034 cm

Step-by-step explanation:

t=3.8 cm s=t/2=3.8/2=1019=1.9 cm  α=47  β=24+30/60=249=24.5   cosα=s:r1  r1=s/cosα=s/cos47° =1.9/cos47° =1.9/0.681998=2.786=2.7859 cm
cosβ=s:r2  r2=s/cosβ=s/cos24.5° =1.9/cos24.5° =1.9/0.909961=2.088=2.088 cm
x=r1 sinα+r2 sinβ=r1 sin47° +r2 sin24.5° =2.7859 sin47° +2.088 sin24.5° =2.7859 0.731354+2.088 0.414693=2.903=2.9034 cm

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