A, B, and C are three points such that $AB = 9 ext{ cm}$, $BC = 11 ext{ cm}$, and $AC = 20 ext{ cm}$. The number of circles passing through points A, B, and C is:

Question

A, B, and C are three points such that $AB = 9 	ext{ cm}$, $BC = 11 	ext{ cm}$, and $AC = 20 	ext{ cm}$. The number of circles passing through points A, B, and C is:

Accepted Answer

**Solution:**

1. Given the points A, B, and C with distances:
   - $AB = 9 	ext{ cm}$
   - $BC = 11 	ext{ cm}$
   - $AC = 20 	ext{ cm}$

2. Check if these points can form a triangle using the triangle inequality theorem:
   - $AB + BC = 9 + 11 = 20$
   - $AC = 20$

3. Since $AB + BC = AC$, the points A, B, and C are collinear (lie on a straight line), and no triangle is formed.

4. A unique circle passing through three points exists only if the points are non-collinear (forming a triangle).

5. Since no triangle is formed, no circle can pass through all three points.

**Answer:** 0

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