Circle's chords

In the circle there are two chord length 30 and 34 cm. The shorter one is from the center twice than longer chord. Determine the radius of the circle.


r =  17.616 cm


t1=30 t2=34 r2=(t1/2)2+(2x)2 r2=(t2/2)2+x2 3x2=(t2/2)2(t1/2)2 x=((t2/2)2(t1/2)2)/3=((34/2)2(30/2)2)/34.6188 r1=(t1/2)2+(2x)2=(30/2)2+(2 4.6188)217.6163 r2=(t2/2)2+(x)2=(34/2)2+4.6188217.6163 r=r1=17.616317.616317.616 cmt_{1}=30 \ \\ t_{2}=34 \ \\ r^2=(t_{1}/2)^2+(2x)^2 \ \\ r^2=(t_{2}/2)^2+x^2 \ \\ 3x^2=(t_{2}/2)^2- (t_{1}/2)^2 \ \\ x=\sqrt{ ((t_{2}/2)^2- (t_{1}/2)^2)/3 }=\sqrt{ ((34/2)^2- (30/2)^2)/3 } \doteq 4.6188 \ \\ r_{1}=\sqrt{ (t_{1}/2)^2+(2x)^2 }=\sqrt{ (30/2)^2+(2 \cdot \ 4.6188)^2 } \doteq 17.6163 \ \\ r_{2}=\sqrt{ (t_{2}/2)^2+(x)^2 }=\sqrt{ (34/2)^2+4.6188^2 } \doteq 17.6163 \ \\ r=r_{1}=17.6163 \doteq 17.6163 \doteq 17.616 \ \text{cm}

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