The radius of the circle is 10 cm and the perpendicular distance from the chord to the centre is 6 cm. Find the length of the chord.

Question

Accepted Answer

Given:
- Radius (r) = 10 cm
- Perpendicular distance from chord to center (d) = 6 cm

We need to find the length of the chord (let it be 2x).

Step 1: Draw the radius to the midpoint of the chord.  
 This forms a right triangle with:  
- Hypotenuse = radius = 10 cm  
- One leg = perpendicular distance from center to chord = 6 cm  
- Other leg = half the chord length = x

Step 2: Use Pythagoras theorem:
  r^2 = d^2 + x^2  
  10^2 = 6^2 + x^2  
  100 = 36 + x^2  
  x^2 = 64  
  x = 8 cm

Step 3: Length of chord = 2x = 2 * 8 = 16 cm

Therefore, the length of the chord is 16 cm.

Answer

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