X, Y, and Z are three points on a plane with XY = 11 cm, YZ = 13 cm, and XZ = 24 cm. The number of circles that travel
through points X, Y, and Z is:

Correct option is A

Given:

A, B, C are three points such that AB = 11 cm, BC = 13 cm, and AC = 24 cm.

Formula used:

For three points to lie on a circle, the sum of the lengths of any two sides must be greater than the third side (Triangle Inequality Theorem).

Solution:
Check triangle inequality for AB, BC, and AC:

AB + BC > AC

11 + 13 > 24

24 = 24 (Not greater)

BC + AC > AB

13 + 24 > 11

37 > 11 (True)

AC + AB > BC

24 + 11 > 13

35 > 13 (True)

Since AB + BC is not greater than AC, the points A, B, C do not form a triangle and hence cannot lie on the same circle. 

Thus, No circle can be formed using the condition.