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