# 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:

$t_{ 1 } = 30 \ \\ t_{ 2 } = 34 \ \\ r^2 = (t_{ 1 }/2)^2+(2x)^2 \ \\ r^2 = (t_{ 2 }/2)^2+x^2 \ \\ 3x^2 = (t_{ 2 }/2)^2- (t_{ 1 }/2)^2 \ \\ x = \sqrt{ ((t_{ 2 }/2)^2- (t_{ 1 }/2)^2)/3 } = \sqrt{ ((34/2)^2- (30/2)^2)/3 } \doteq 4.6188 \ \\ r_{ 1 } = \sqrt{ (t_{ 1 }/2)^2+(2x)^2 } = \sqrt{ (30/2)^2+(2 \cdot \ 4.6188)^2 } \doteq 17.6163 \ \\ r_{ 2 } = \sqrt{ (t_{ 2 }/2)^2+(x)^2 } = \sqrt{ (34/2)^2+4.6188^2 } \doteq 17.6163 \ \\ r = r_{ 1 } = 17.6163 \doteq 17.6163 = 17.616 \ \text { cm }$

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