Concentric circles and chord

In a circle with a diameter d = 10 cm, a chord with a length of 6 cm is constructed. What radius have the concentric circle while touch this chord?

Result

r2 =  4 cm

Solution:

d=10 cm t=6 cm  r1=d/2=10/2=5 cm  r12=r22+(t/2)2  r2=r12−(t/2)2=52−(6/2)2=4 cmd=10 \ \text{cm} \ \\ t=6 \ \text{cm} \ \\ \ \\ r_{1}=d/2=10/2=5 \ \text{cm} \ \\ \ \\ r_{1}^2=r_{2}^2 + (t/2)^2 \ \\ \ \\ r_{2}=\sqrt{ r_{1}^2 - (t/2)^2 }=\sqrt{ 5^2 - (6/2)^2 }=4 \ \text{cm}

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