To divide a line segment AB in the ratio 5 : 7, first a ray AX is drawn so that ∠BAX is an acute angle and then equidistant points are marked on the ray AX in such a way that the minimum number of these points is

Explanation -

Let's approach this differently to find the minimum number of equidistant points on ray AX to divide the line segment AB in the ratio 5:7.

To divide the line segment AB in the ratio 5:7 using an acute angle ∠BAX and marking equidistant points on the ray AX, the process involves creating 12 equal parts along the ray AX.

Each part represents one division, and since the ratio is 5:7 (total of 5 + 7 = 12 parts).

The minimum number of equidistant points would indeed be 12.

Therefore, the correct answer is 12.