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
Attached Figure / Diagram
A
32cm
B
26cm
C
20cm
D
16cm
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
\(\bigtriangleup\)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
Source: WAEC / JAMB / NECO Classroom Archive (Record #33092)