Question

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

11th - 12th Class

Maths

Solution

136

4.0 (1 ratings)

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} )