19. From the centre of a circle, di...
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19. From the centre of a circle, distance of a chord is 16 cm. If radius of the circle be 20 cm. What will be the length of the chord? (1) 6 cm (2) 12 cm (3) 24 cm (4) 36 cm

11th - 12th Class
Maths
Solution
101
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19. (3) According to the question, and, ( therefore ) In right angled ( Delta O M A ) [ begin{aligned} (O A)^{2} &=(O M)^{2}+(A M)^{2} Rightarrow quad(A M)^{2} &=(O A)^{2}-(O M)^{2} Rightarrow quad(A M)^{2} &=(20)^{2}-(16)^{2} &=400-256=144 end{aligned} ] ( Rightarrow quad A M=12 mathrm{cm} ) Thus, length of chord, ( A B=2 . A M=2 times 12=24 mathrm{cm} )
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