Option A
Length of CD is 10 inches
Solution:
The diagram is attached below
Given that, Circle A and circle B are congruent
CD is a cord of both circles
AB = 24 inches
Radius = 13 inches
To find: length of CD
Draw a straight line connecting A and C
AC represents the radius of circle. Also given that radius is 13 inches, So AC = 13 inches
Given in question that AB = 24 inches
Therefore from figure, AO = AB/2 = 24/2 = 12
AO = 12
Let "b" be the length of CO
Therefore, CD = CO + OD = b + b
AOC forms a triangle, so we can use pythogoras theorem
Pythagorean theorem, states that the square of the length of the hypotenuse is equal to the sum of squares of the lengths of other two sides of the right-angled triangle.
By above definition for triangle AOC
[tex]AC^2 = AO^2 + OC^2[/tex]
Substituting AC = 13 and AO = 12 and OC = b
[tex]13^2 = 12^2 + b^2\\\\b^2 = 169 - 144\\\\b^2 = 25\\\\b = 5[/tex]
Thus length of CD is:
CD = b + b = 5 + 5 = 10
Thus length of CD is 10 inches
