Multiple choice

Two circles with the centres A and B of radii 3 cm and 4 cm respectively intersect at two points C and D such that AC and BC are tangents to the two circle. Find the length of the common chord CD.

  1. 3.5

  2. 3.9

  3. 4.5

  4. 4.8

  5. None of these
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Two circles intersect, AC is tangent to circle B, BC is tangent to circle A. So AC ⊥ AB and BC ⊥ AB. Triangle ABC has AB = 3+4 = 7 cm, AC = 3 cm, BC = 4 cm (right triangle by Pythagoras: 3² + 4² = 5²). CD is common chord perpendicular to AB. Using chord properties: CD = 2 × √(3² - (3×5/7)²) ≈ 4.8 cm.

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