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Question 9 : Let C be a circle of radius 5 meters having center at O. Let PQ be a chord of C that passes through points A and B where A is located 4 meters north of O and B is located 3 meters east of O. Then, the length of PQ, in meters, is nearest to

  1. 6.6
  2. 7.2
  3. 8.8
  4. 7.8

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Explanatory Answer

Triangle inscribed in Circle
Right Triangle
O is the center of the circle and radius of circle = 5
In triangle AOB, using pythagorean triplet AB = 5
OR = \\frac{3 × 4}{5}) = 2.4
Since OR if from the center it bisects the chord,
Now in triangle POR,
52 = PR2 + (2.4)2
PR = √{19.24}
PQ = 2 √{19.24}
PQ ≅ 8.8

The answer is, "8.8"

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