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
Attached Figure / Diagram
A
3cm
B
4cm
C
5cm
D
8cm
E
15cm
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
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
Source: Myschool Past Questions Archive (Record #22360)