In the diagram EFGH is a circle centre O FH is ... - JAMB Mathematics 2000 Question

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

(\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