Question on: JAMB Mathematics - 2000

In the diagram, EFGH is a circle centre O. FH is a diameter and GE is a chord which meets FH at right angle at the point N. If NH = 8cm and EG = 24cm, calculate FH
A
32cm
B
26cm
C
20cm
D
16cm
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Correct Option: B

(\bigtriangleup)OEN = (\bigtriangleup)OGN

OE = OG = r(radii)

(r - 8)2 + 122 = r2

r2 - 16r + 64 + 144 = r2

16r = 64 + 144 = r2

16r = 64 + 144 = 208

(\frac{208}{16}) = 13cm

FH = 2FO = 2OH = 2R

= 2 x 13cm

= 26cm

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