Mathematics

In the diagram above, O is the center of the circle. Calculate the length of…

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
Correct Answer: Option D
Explanation

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