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.

Result

r =  17.616 cm

Solution:

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)/3≐4.6188 r1=(t1/2)2+(2x)2=(30/2)2+(2⋅ 4.6188)2≐17.6163 r2=(t2/2)2+(x)2=(34/2)2+4.61882≐17.6163 r=r1=17.6163≐17.6163=17.616  cm t_{ 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 = 17.616 \ \text { cm }

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Following knowledge from mathematics are needed to solve this word math problem:

Pythagorean theorem is the base for the right triangle calculator.

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