Two chords

In a circle with radius r = 26 cm two parallel chords are drawn. One chord has a length t1 = 48 cm and the second has a length t2 = 20 cm, with the center lying between them. Calculate the distance of two chords.

Result

x =  34 cm

Solution:

r=26 cm t1=48 cm t2=20 cm  x1=r2(t1/2)2=262(48/2)2=10 cm x2=r2(t2/2)2=262(20/2)2=24 cm  x=x2+x1=24+10=34 cmr=26 \ \text{cm} \ \\ t_{1}=48 \ \text{cm} \ \\ t_{2}=20 \ \text{cm} \ \\ \ \\ x_{1}=\sqrt{ r^2 - (t_{1}/2)^2 }=\sqrt{ 26^2 - (48/2)^2 }=10 \ \text{cm} \ \\ x_{2}=\sqrt{ r^2 - (t_{2}/2)^2 }=\sqrt{ 26^2 - (20/2)^2 }=24 \ \text{cm} \ \\ \ \\ x=x_{2}+x_{1}=24+10=34 \ \text{cm}



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