To solve for the length from point A to point B, we first need to analyze the situation using geometry.
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Identify the known values:
- The radius of the clock (circle) is 20 cm. Therefore, the distance from the center E of the clock to points A and C (where the tangents touch the circle) is 20 cm.
- The distance from the top of the clock at point D to the hanger at point B is 5 cm.
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Determine the lengths from the center E to point D and point B:
- The distance from the center E to point D (the top of the clock) is also equal to the radius of the clock, which is 20 cm.
- Therefore, the total distance from point E to point B can be calculated as: \[ \text{Distance from E to B} = \text{Distance from E to D} + \text{Distance from D to B} = 20 \text{ cm} + 5 \text{ cm} = 25 \text{ cm} \]
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Using right triangle properties:
- Since segments AB and BC are tangents to the circle at points A and C, triangle EAB is a right triangle.
- In right triangle EAB, we have:
- EB (hypotenuse) = 25 cm (calculated above)
- EA (radius, one leg) = 20 cm
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Applying the Pythagorean theorem: To find AB (the tangent segment), we can use: \[ EB^2 = EA^2 + AB^2 \] Plugging in the values we know: \[ 25^2 = 20^2 + AB^2 \] This simplifies to: \[ 625 = 400 + AB^2 \] \[ AB^2 = 625 - 400 = 225 \] \[ AB = \sqrt{225} = 15 \text{ cm} \]
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Conclusion: Therefore, the length from point A to point B is:
\[ \boxed{15 \text{ cm}} \]
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