Question

The given figure shows two concentric circles and AD is a chord. The relation between AB and CD is:

Options

• AB = CD

• AB > CD

• AB < CD

• AB ≠ CD

Answer 1

AB = CD

Explanation:

• Draw a perpendicular from the centre O to the chord AD, intersecting the line at point M (OM ⊥ AD).
• The perpendicular from the centre of a circle to a chord bisects the chord. Therefore, for the outer circle, the perpendicular bisects chord AD, giving:
  AM = MD
• Similarly, for the inner circle, the same perpendicular bisects chord BC, giving:
  BM = MC
• The segment AB can be expressed as the difference between AM and BM:
  AB = AM − BM
• Likewise, the segment CD can be expressed as:
  CD = MD − MC
• Since AM = MD and BM = MC, it follows that:
  AB = CD