Find the length of a chord which subtends an angle of 90^\circ at the centre of a circle whose radius is 8 cm.
A
\(8\sqrt{3}\) cm
B
4 cm
C
8 cm
D
\(8\sqrt{2}\) cm
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
Length of chord = \(2r \sin (\frac{\theta}{2})\)
= \(2 \times 8 \times \sin (\frac{90}{2})\)
= \(16 \times \frac{\sqrt{2}}{2}\)
= \(8\sqrt{2} cm\)
Source: Myschool Past Questions Archive (Record #54919)