Multiple choice

AD is a diameter of a circle and AB is a chord. If $AD = 34 cm\ and\ AB = 30$ cm, the distance of AB from the centre of the circle is

  1. 17cm

  2. 15cm

  3. 4cm

  4. 8cm
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D Correct answer
Explanation

The radius r = 34 / 2 = 17 cm. A chord AB of 30 cm is at a distance d from the center. Using the Pythagorean theorem in the triangle formed by the radius, half the chord, and the distance d: d^2 + (30/2)^2 = 17^2. d^2 + 15^2 = 17^2, d^2 + 225 = 289, d^2 = 64, d = 8 cm.

AI explanation

The radius of the circle is half the diameter, so the radius is 34 divided by 2, which is 17 cm. A line drawn from the center perpendicular to the chord bisects the chord, creating a right triangle with a hypotenuse of 17 and a base of 15 (half of 30). Using the Pythagorean theorem, the distance is the square root of (17 squared minus 15 squared), which is the square root of (289 minus 225), equaling 8 cm.

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