In the diagram above, O is the center of the circle. Calculate the length of the chord AB if |OA| = 5cm, |OD| = 3cm and ∠AOD = ∠BOD

  • A 3cm
  • B 4cm
  • C 5cm
  • D 8cm
  • E 15cm
waec 1989mathematics

The correct answer is D. 8cm

In \(\Delta DOB\), let < DOB = \(\alpha\)

In \(\Delta DOB\), \(5^2 = 3^2 + s^2\)

\(s^2 = 25 - 9 = 16\)

\(s = 4cm\)

\(\sin \alpha = \frac{4}{5}\)

\(\alpha = \frac{< AOB}{2}\)

Length of chord = \(2r \sin (\frac{\theta}{2})\)

|OB| = r = 5cm

L = \(2(5)(\frac{4}{5})\)

= 8 cm

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