Multiple choice

Directions : Select the correct alternative from the given choices. Two circles, C1 and C2, each of radius 3 cm, with centres at X and Y respectively, intersect each other such that the line XY joining the centres intersects the circles C1 and C2 at P and Q respectively and PQ = 2 cm. lf the whole assembly is enclosed in a rectangle of minimum possible area, the perimeter of the rectangle is

  1. 28 cm

  2. 32 cm

  3. 40 cm

  4. 60 cm
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The distance between centers XY = 3+3-2 = 4 cm. The rectangle width is 2 * radius = 6 cm. The length is 2 * radius + XY = 6 + 4 = 10 cm. Perimeter = 2 * (6 + 10) = 32 cm.

AI explanation

The minimum bounding rectangle must span the horizontal distance PQ plus the two radii extending to the left and right, making the length 2 cm + 3 cm + 3 cm = 8 cm. The width of this rectangle equals the diameter of the circles, which is 2 * 3 cm = 6 cm. The perimeter of a rectangle is 2*(length + width), so 2*(8 + 6) = 32 cm.

Keep practicing — related questions