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Given two concetric circles with centre ...

Given two concetric circles with centre O. A line cut the circle at A,B,C and D respectively. If AB=10cm, then find the length of CD.

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To solve the problem of finding the length of CD given that AB = 10 cm in two concentric circles with center O, we can follow these steps: ### Step-by-Step Solution: 1. **Understand the Configuration**: We have two concentric circles with the same center O. A line intersects these circles at points A, B, C, and D. 2. **Identify the Segments**: The line segment AB is the chord of the outer circle, and the line segment CD is the chord of the inner circle. 3. **Use the Property of Chords in Concentric Circles**: In concentric circles, if a line intersects both circles, the lengths of the chords created by that line will be equal. This is because the distance from the center to the line is the same for both circles. 4. **Given Information**: We know that the length of the chord AB in the outer circle is 10 cm. 5. **Conclusion**: Since the lengths of the chords AB and CD are equal in concentric circles, we can conclude that the length of chord CD is also 10 cm. ### Final Answer: The length of CD is 10 cm. ---
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