Common chord

Two circles with radius 17 cm and 20 cm are intersect at two points. Its common chord is long 27 cm. What is the distance of the centers of these circles?

Result

l =  25.1 cm

Solution:

 l12=r12(t/2)2 l22=r22(t/2)2  l=l1+l2 l=1722724+2022724=25.1 cm \ \\ l_1^2 = r_1^2 - (t/2)^2 \ \\ l_2^2 = r_2^2 - (t/2)^2 \ \\ \ \\ l = l_1 + l_2 \ \\ l = \sqrt{ 17^2- \dfrac{ 27^2}{4} } + \sqrt{ 20^2 - \dfrac{ 27^2}{4}} = 25.1 \ \text{cm}



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