Multiple choice

If a chord of length 8 cm is situated at a distance of 3cm from centre, then the diameter of circle is:

  1. 11 cm

  2. 10 cm

  3. 12 cm

  4. 15 cm
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A perpendicular from the center to a chord bisects the chord. Using the Pythagorean theorem on the triangle formed by the radius (r), the distance from the center (3 cm), and half the chord (4 cm), we get r^2 = 3^2 + 4^2 = 25, so r = 5 cm. The diameter is 2 * r = 10 cm.

AI explanation

A line from the center of a circle perpendicular to a chord bisects the chord, creating a right triangle with a leg of 4 cm and another leg of 3 cm. Using the Pythagorean theorem, the radius r is calculated as the square root of 4 squared plus 3 squared, which equals the square root of 25, or 5 cm. Since the diameter is twice the radius, the diameter of the circle is 10 cm.

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