Multiple choice

The length of the chord of circle whose radius is $5cm$ and perpendicular distance from center is $4cm$

  1. $3$
  2. $6$
  3. $5$
  4. $4$
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B Correct answer
Explanation

The radius, the perpendicular distance from the center to the chord, and half the chord length form a right-angled triangle. Using the Pythagorean theorem, half the chord length is sqrt(5^2 - 4^2) = sqrt(25 - 16) = 3. Thus, the full chord length is 2 * 3 = 6.

AI explanation

Using the property of circles, the perpendicular from the center to a chord bisects the chord, forming a right triangle with the radius and half the chord. The half-length is found using the Pythagorean theorem: square root of (5 squared minus 4 squared) equals 3. The total length of the chord is twice this half-length, so 2 multiplied by 3 is 6.

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