Question

What is the distance between the center of a circle and a chord that is 30 cm long if the diameter is 32 cm long?

Answer 1

• 
  `√(31) \ cm`

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Midpoint of the chord, one of the endpoints of the chord and the center form a right triangle with the radius being its hypotenuse.

The sides of the triangle are:

• One leg is the half-chord, 30/2 = 15 cm;
• Hypotenuse is the half-diameter, 12/2 = 16 cm;
• The other leg is the distance from the center to the chord, x cm.

Use Pythagorean theorem to find the value of x:

• 
  `x=√(16^2-15^2)`
• 
  `x=√(31)`