In a circle radius rcm, a chord 16\(\sqrt{3}cm\) long is 10cmfrom the centre of the circle. Find, correct to the nearest cm, the value of r
A
22cm
B
17cm
C
16cm
D
15cm
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
In the diagram
|AM| = |MB| - \(\frac{|AB|}{2}\)
= \(\frac{16\sqrt{3}}{2}\)cm
= 8\(\sqrt{3}\)cm
in \(\Delta\) AMO, r2 = |AM|Z + |MO|2
r2 = (8\(\sqrt{3}\))2
+ 102
= 64 x 3 + 100
= 192 + 100
= 292
r = \(\sqrt{292}\)
17.088cm
17cm
Source: Myschool Past Questions Archive (Record #46027)