Math Problem Statement
AD is the diameter of a circle of radius 17cm and AB is of length 30 cm. Find the distance of AB from the centre.
Solution
To find the distance of line segment from the center of the circle, we can use the following steps:
-
Identify key components:
- The radius of the circle cm.
- The diameter cm.
- The length of segment cm.
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Use the right triangle relationship:
- Let be the center of the circle.
- The distance from to is the perpendicular distance we want to find, denoted as .
- The midpoint of is where the perpendicular from meets .
-
Apply the Pythagorean theorem:
- The distance from the center to point is equal to the radius, which is cm.
- The length (half of ) is cm.
Using the Pythagorean theorem in triangle :
Thus, the distance of from the center of the circle is 8 cm.
Do you want details or have any questions?
Here are some related questions you might find interesting:
- What would happen to the distance if the length of were greater than the diameter?
- How do you find the area of the circle given the radius?
- Can you explain how to find the angle subtended by chord at the center?
- What are other methods to find the distance from a point to a line?
- How would the situation change if were a secant line instead?
Tip: Always remember to check whether a line segment lies entirely within the circle or intersects it to apply the right geometric principles.
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Math Problem Analysis
Mathematical Concepts
Geometry
Circle Properties
Pythagorean Theorem
Formulas
Diameter = 2 * Radius
Pythagorean Theorem: OA^2 = OM^2 + AM^2
Theorems
Pythagorean Theorem
Suitable Grade Level
Grades 7-9
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