Madhya Pradesh Police Exam Model Paper 6

Given:
Diameter of circle = 26cm
Radius OA = 13cm
Length of chord AB = 10cm
Concepts used:
perpendicular drawn from the centre of the circle to the chord, bisects the chord
Calculation:
$\mathit{A}\mathit{C}=\mathit{A}\mathit{B}/2=10/2=5\mathit{c}\mathit{m}$ ….(⊥ drawn from the centre of the circle, bisects the chord)
using Pythagorean Theorem
$\mathit{O}{\mathit{A}}^2=\mathit{O}{\mathit{C}}^2+\mathit{A}{\mathit{C}}^2$
$\Rightarrow 132=\mathit{O}{\mathit{C}}^2+52$
$\Rightarrow 169=\mathit{O}{\mathit{C}}^2+25$
$\Rightarrow \mathit{O}{\mathit{C}}^2=144$
OC = 12cm
∴ The perpendicular distance of the chord from centre is 12 cm