Question

The line joining the centre of a circle to the mid-point of a chord is always perpendicular to the chord. True or False?

• A. True
• B. False

Answer 1

The correct option is A True



Let the centre of a circle be O.
OA and OB are radii
AB is any chord with D as the midpoint.
In $\Delta AODand\Delta BOD$,
OA = OB (radius)
AD = BD (D is mid point of AB)
OD = OD (Common)
$\therefore \Delta AOD\cong \Delta BOD\left(SSS\right)$
$\Rightarrow \angle ODA=\angle ODB$
But they are linear pair.
$\therefore \angle ODA=\angle ODB={90}^{\circ }$
$\Rightarrow OD\perp AB$