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
Correct answer is 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