The diameter AB, equal to 6 cm, is drawn in the circle. A tangent parallel to this diameter touches the circle at point M.
| March 17, 2021 | education
The diameter AB, equal to 6 cm, is drawn in the circle. A tangent parallel to this diameter touches the circle at point M. Find the length of the line segment AM.
Given: a circle,
AB – diameter.
AB = 6 cm.
tangent // AB (at point M).
Find: segment AM.
Decision.
1. By the circle tangent theorem, the tangent is perpendicular to the radius of the circle.
2. The segment AM is the radius of the circle, since it connects the center and the extreme point of the circle.
3. Therefore, AM = 6 cm / 2 = 3 centimeters.
Answer: AM = 3 centimeters.
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