Multiple choice

If the length of the common chord of two intersecting equal circles be 6 cm and if the radius of each circle be 5 cm then the distance between the centers of the circle is

  1. 7 cm

  2. 8 cm

  3. 9 cm

  4. none
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The common chord divides the line connecting the centers into two equal parts (3 cm each) and is perpendicular to it. Using the Pythagorean theorem in one of the triangles formed by the radius, half the chord, and the distance from the center to the chord: d^2 + 3^2 = 5^2, so d = 4. The distance between centers is 2d = 8 cm.

AI explanation

The common chord acts as the base of two identical isosceles triangles formed with the two centers, so the line of centers perpendicularly bisects the 6 cm common chord. Using the Pythagorean theorem, the distance from one center to the chord is sqrt(5^2 - 3^2) = sqrt(25 - 9) = 4 cm. Since the circles are equal, the distance from the other center to the chord is also 4 cm. The total distance between the centers is the sum of these distances, giving 4 cm + 4 cm = 8 cm.

Keep practicing — related questions