If the radius of a circle is 30cm. Find the length of a chord which is 10cm from the center?
Answer: 40√2
Explanation
To find the length of the chord:
Let's denote the chord's length as 2x (since x would be half the chord's length due to symmetry).
The distance from the center to the chord is 10cm, forming a right triangle with hypotenuse 30cm (radius) and one leg 10cm (distance to chord).
The other leg (x) can be found using the Pythagorean theorem:
x² + 10² = 30²
x² + 100 = 900
x² = 800
x = √800 = √(400*2) = 20√2
The full chord's length is 2x = 2 * 20√2 = 40√2
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