A, B, C are three points so that AB = 4 cm, BC = 6 cm and AC = 10 cm. The number of circles passing through the points A, B, C is:

0 

We know that,

Property of formation of triangle is;

Sum of any two sides must be greater than the 3rd side.

i.e. a + b > c where a, b, c are three sides of the triangle.

According to the question,

A, B, C three points.

AB = 4 cm

BC = 6 cm

AC = 10 cm

AB + BC = AC

No triangle can be formed using the three sides given so, No circle will pass through the points A, B, C.