Question

sol. (1)
Let ( mathrm{OE}=x mathrm{cm} )
then ( mathrm{OF}=(x+1) mathrm{cm} )
[
begin{array}{l}
O A=O C=r mathrm{cm}
A E=4 mathrm{cm} ; C F=3 mathrm{cm}
end{array}
]
From ( Delta ) OAE,
[
mathrm{OA}^{2}=mathrm{AE}^{2}+mathrm{OE}^{2}
]
( Rightarrow r^{2}=16+x^{2} )
( Rightarrow quad x^{2}=r^{2}-16 )
From ( Delta mathrm{OCF} )
( (x+1)^{2}=r^{2}-9 )
(ii)
By equation (ii) ( - ) (i), ( (x+1)^{2}-x^{2}=r^{2}-9-r^{2}+16 )
( Rightarrow 2 x+1=7 Rightarrow x=3 mathrm{cm} )
( therefore ) From equation (i), ( 9=r^{2}-16 Rightarrow r^{2}=25 Rightarrow r=5 mathrm{cm} )

# Ex. 1. AB = 8 cm and CD = 6 cm are two parallel chords on the same side of the centre of a circle. The distance between them is 1 cm. The radius of the circle is (1) 5 cm (2) 4 cm (3) 3 cm (4) 2 cm

Solution