The circles and intersect at two points. The length of their common chord is

Answer and explanation

Correct answer: A. 24

  1. Step 1: Identify the centres and radii of the two circles: with , and with . The distance between the centres is .
  2. Step 2: In the triangle formed by and an intersection point , the side lengths are . The semi-perimeter is . By Heron's formula, the area is .
  3. Step 3: The distance from to the line of centres is the semi-chord length: . Therefore, the total length of the common chord is .
Answer
24.

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