Question 26

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Jambmaths question: 

In the diagram above , EFGH is a circle, centre O, FH is a diameter and GE is a chord, which meets FH at right angle at point N. If NH is 8cm and EG= 24cm. Calculate FH

Option A: 

16cm

Option B: 

20cm

Option C: 

26 cm

Option D: 

32cm

Jamb Maths Solution: 

$\begin{align}  & r=OE=OF=OG=OH\text{      }\!\!\{\!\!\text{ radius of circle }\!\!\}\!\!\text{ } \\ & NO=x \\ & OH=8+x,\text{   }OE=OF=OG=8+x \\ & O{{G}^{2}}=O{{N}^{2}}+N{{G}^{2}} \\ & {{(8+x)}^{2}}={{x}^{2}}+{{12}^{2}} \\ & {{x}^{2}}+16x+64={{x}^{2}}+144 \\ & 16x=80 \\ & x=5 \\ & FH=2(r)=2(OH)\text{    }\!\!\{\!\!\text{ Diameter of a circle }\!\!\}\!\!\text{ } \\ & FH=2(8+x) \\ & FH=2(8+5)=2\times 13=26 \\\end{align}$

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