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O is the center of a circle. The radius of the circle is 26cm. The distance from O to the mid-point of chord AB is 24cm. Work out the length of chord AB :)
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Respuesta :

Answer:

20 cm

Step-by-step explanation:

Picture the scenario in your mind.

The figure will be a right triangle, where the hypotenuse is the radius, and the first altitude will be the distance between the center and the chord, and the second altitude will be half the chord length.

So, to find the length of the chord :

  • (1/2 chord length)² + (distance b/w center and midpoint of AB)² = (radius)²
  • chord length² / 4 = (26)² - (24)²
  • chord length² / 4 = 676 - 576
  • chord length² = 100 × 4
  • chord length = 20 cm

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