Multiple choice

A chord is 5 cm away from the center of the circle. The length of the chord and the diameter of the circle is in the ratio of 4: 5, find the diameter of the circle.

  1. 20/3

  2. 25/3

  3. 40/3

  4. 50/3
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D Correct answer
Explanation

Using the chord property: in a circle, the perpendicular from the center bisects the chord. If radius = r, then (chord/2)² + 5² = r² by Pythagoras. Given chord : diameter = 4 : 5, chord = 4k and diameter = 5k, so r = 2.5k. Then (2k)² + 25 = (2.5k)², giving 4k² + 25 = 6.25k², so 2.25k² = 25, k² = 25/2.25 = 100/9, and k = 10/3. Diameter = 5k = 50/3.

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