Three points X:Y and Z are concyclic to the largest circle with radius 15 cm and there is another concentric circle with radius 8 cm such that XY and XZ are tangents to the smaller circle. At how many points does YZ intersect the larger circle?

Options

A. 0
B. 1
C. 2
D. can't say

Answer

To solve the problem, we need to analyze the given information about the circles and the points X, Y, and Z.

### Step-by-Step Solution:

1. **Understanding the Circles**:
- We have two concentric circles:
- The larger circle with a radius of 15 cm.
- The smaller circle with a radius of 8 cm.

2. **Identifying the Points**:
- Points X, Y, and Z are concyclic, meaning they lie on the circumference of the larger circle.

3. **Tangents to the Smaller Circle**:
- The segments XY and XZ are tangents to the smaller circle. By the properties of tangents, these segments will touch the smaller circle at exactly one point each.

4. **Analyzing the Line YZ**:
- The line segment YZ connects points Y and Z. Since both Y and Z are on the circumference of the larger circle, we need to determine how many times this line intersects the larger circle.

5. **Intersection Points**:
- The line segment YZ will intersect the larger circle at two points: one point at Y and another point at Z.

6. **Conclusion**:
- Therefore, the line segment YZ intersects the larger circle at exactly two points.

### Final Answer:
The line segment YZ intersects the larger circle at **2 points**.