Multiple choice

If the lengths of two parallel chords in a circle of radius 10 cm are 12 cm and 16 cm, then what is the distance between these two chords?

  1. 1 cm or 7 cm

  2. 2 cm or 14 cm

  3. 3 cm or 21 cm

  4. 4 cm or 28 cm
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Distance from center to chords: d1 = sqrt(10^2 - 6^2) = 8. d2 = sqrt(10^2 - 8^2) = 6. If chords are on the same side, distance = 8 - 6 = 2. If on opposite sides, distance = 8 + 6 = 14.

AI explanation

A perpendicular from the center to the 12 cm chord forms a right triangle with a hypotenuse of 10 and a base of 6. Using the Pythagorean theorem, the distance from the center to this chord is the square root of (100 minus 36), which is 8 cm. For the 16 cm chord, the base is 8, so its distance from the center is the square root of (100 minus 64), which is 6 cm. If the chords are on opposite sides of the center, the distance is 8 plus 6, and if they are on the same side, it is 8 minus 6, giving 14 cm or 2 cm.

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