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Two circles C1 and C2 having the same radius of 2 cm and centres at P and Q respectively intersect each other such that the line of centres PQ intersects C1 and C2 at F and E respectively. EF = 1 cm. The whole assembly is enclosed in a rectangle of minimum area. The perimeter of rectangle is:
- a)20 units
- b)22 units
- c)24 units
- d)26 unit
- e)28 units
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
Two circles C1 and C2 having the same radius of 2 cm and centres at P...
Given Information:
- Radius of circles C1 and C2 = 2 cm
- EF = 1 cm
Solution:
Finding the Perimeter of the Rectangle:
To find the perimeter of the rectangle enclosing the circles, we need to consider the diameter of the circles. Since the line of centers PQ intersects both circles at points E and F, the line EF represents the diameter of the circles.
Finding the Diameter:
Since the radius of the circles is 2 cm, the diameter of the circles is 2 * 2 = 4 cm.
Given that EF = 1 cm, we can find the length of the line PQ using the Pythagorean theorem:
PQ^2 = EF^2 + (2 * 2)^2
PQ^2 = 1^2 + 4^2
PQ^2 = 1 + 16
PQ = √17 cm
Finding the Perimeter of the Rectangle:
The perimeter of the rectangle is twice the sum of the sides of the rectangle, which can be calculated as:
Perimeter = 2 * (2 * PQ + 2 * 2)
Perimeter = 2 * (2 * √17 + 4)
Perimeter = 2 * (2√17 + 4)
Perimeter = 4√17 + 8 ≈ 22 units
Therefore, the perimeter of the rectangle enclosing the circles is approximately 22 units, which corresponds to option B.
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Community Answer
Two circles C1 and C2 having the same radius of 2 cm and centres at P...
Length of rectangle = 2 x diameter = EF = 8 - 1 = 7
Breadth of rectangle = diameter = 4
So Perimeter = 2 x (7+4) = 22
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Two circles C1 and C2 having the same radius of 2 cm and centres at P and Q respectively intersect each other such that the line of centres PQ intersects C1 and C2 at F and E respectively. EF = 1 cm. The whole assembly is enclosed in a rectangle of minimum area. The perimeter of rectangle is:a)20 unitsb)22 unitsc)24 unitsd)26 unite)28 unitsCorrect answer is option 'B'. Can you explain this answer?
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