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Directions: Kindly study the following questions carefully and choose the right answer:
Two equal circles of radius 4 cm intersect each other such that each passes through the centre of the other. The length of the common chord is :
  • a)
    2√3 cm
  • b)
    4√3 cm
  • c)
    2√2 cm
  • d)
    8 cm
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
Directions: Kindly study the following questions carefully and choose ...
According to question , we draw a figure of two equal circles of radius 4 cm intersect each other such that each passes through the centre of the other ,

OC = 2cm
OA = 4cm
∴ AC = √OA² - OC²
∴ AC = √4² - 2² = √16 - 4
AC = √12 = 2√3
∴ AB = 4√3cm
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Community Answer
Directions: Kindly study the following questions carefully and choose ...
Explanation:

Given:
- Two equal circles of radius 4 cm intersect each other such that each passes through the centre of the other.

Common Chord:
- When two circles intersect in such a way that each circle passes through the center of the other, the line joining the points of intersection is called a common chord.

Properties of Common Chord:
- The common chord is perpendicular to the line joining the centers of the circles.
- It bisects the line joining the centers of the circles.

Calculation:
- In this case, since the circles have the same radius and intersect at the center of each other, the common chord will be the diameter of each circle.
- The diameter of a circle is equal to twice the radius.
- Therefore, the length of the common chord is 2 * 4 cm = 8 cm.
Therefore, the length of the common chord is 8 cm.
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Directions: Kindly study the following questions carefully and choose the right answer:Two equal circles of radius 4 cm intersect each other such that each passes through the centre of the other. The length of the common chord is :a)2√3 cmb)4√3 cmc)2√2 cmd)8 cmCorrect answer is option 'B'. Can you explain this answer?
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