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      Question

      Consider two concentric circles having radii 17 cm and

      15 cm. What is the length (in cm) of the chord, of the bigger circle, which is a tangent to the smaller circle?
      A 12 Correct Answer Incorrect Answer
      B 16 Correct Answer Incorrect Answer
      C 10 Correct Answer Incorrect Answer
      D 8 Correct Answer Incorrect Answer

      Solution

      Given:   Radius of circles r1= 15 cm   r2= 17 cm Property of tangent - A tangent is perpendicular to the center of the circle. Property of chord - A perpendicular line drawn from the center of the circle to the chord of the circle always divide the chord in half. Applying the property of chord and tangent: We find that- 172 = 152+(x/2)2 289 = 225 +x2 /4 289 – 225 =x2 /4 x2 =256 x=16  Therefore, length of the chord = 16 cm.

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