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

Question

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

Accepted Answer

**Solution:**

1. The number of circles passing through three points depends on whether the points are collinear or not.

2. If the points are collinear, no circle can pass through all three points because a circle requires three non-collinear points to define it uniquely.

3. Check if points X, Y, and Z are collinear by verifying if the sum of two sides equals the third side:
   - $XY + YZ = 11 + 13 = 24$
   - $XZ = 24$

4. Since $XY + YZ = XZ$, the points lie on a straight line, i.e., they are collinear.

5. Therefore, no circle can pass through all three points.

**Answer:** 0

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