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
waec 2015mathematics

The correct answer is B. 17cm

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

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