JAMB - Mathematics (2000 - No. 41)
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
32cm
26cm
20cm
16cm
Explanation
\(\bigtriangleup\)OEN = \(\bigtriangleup\)OGN
OE = OG = r(radii)
(r - 8)\(^2\) + 12\(^2\) = r\(^2\)
r\(^2\) - 16r + 64 + 144 = r\(^2\)
16r = 64 + 144
16r = 64 + 144 = 208
\(\frac{208}{16}\) = 13cm
FH = 2FO = 2OH = 2R
= 2 x 13cm
= 26cm
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