Question

Circle A and circle B are congruent. CD is a cord of both circles. if AB = 24 inches in the radius is 13 inches how long is CD A.10in B.26in C.12in D.9in

Answer 1

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

$AC^2 = AO^2 + OC^2$

Substituting AC = 13 and AO = 12 and OC = b

$13^2 = 12^2 + b^2\\\\b^2 = 169 - 144\\\\b^2 = 25\\\\b = 5$

Thus length of CD is:

CD = b + b = 5 + 5 = 10

Thus length of CD is 10 inches