Math Problem Statement
Solution
To solve this problem, let's analyze the geometry in the circle and apply appropriate calculations.
Given Information:
- We need to find the length of the chord .
Solution Approach:
-
Determine the Radius : Since is the center of the circle and is a radius, we have:
-
Identify Triangle : Triangle is a right triangle with:
- as one leg,
- as the other leg,
- as the hypotenuse.
-
Calculate Using the Pythagorean Theorem: Substituting the values:
-
Determine : Since is a chord perpendicular to at , and is the midpoint of , we can calculate using the formula for a chord: Substituting the values:
Answer:
The length of chord is , which corresponds to option A. 16 cm.
Do you want more details or have any questions?
Here are five related questions to explore further:
- How do we calculate the radius of a circle if given only a chord and a perpendicular distance from the center?
- What other methods can we use to find the length of a chord in a circle?
- How would the length of change if the radius of the circle was different?
- What is the significance of the Pythagorean theorem in solving circle problems?
- Can this problem be solved using trigonometric methods?
Tip: For problems involving chords in a circle, drawing perpendiculars from the center can often simplify calculations significantly.
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Math Problem Analysis
Mathematical Concepts
Geometry
Circles
Chords
Formulas
Pythagorean theorem: a^2 + b^2 = c^2
Chord length formula: AB = 2 * sqrt(OC^2 - OE^2)
Theorems
Pythagorean theorem
Suitable Grade Level
Grades 10-12