Question

A circle has a radius of 5 cm and a chord AB of 8 cm. How far is the midpoint of the chord from the centre of the circle?

• A. 5 cm
• B. 4 cm
• C. 3 cm
• D. 2.5 cm

Answer 1

The correct option is C 3 cm

Consider the above circle wherein OB = 5 cm (radius of the circle) and AB = 8 cm.
We know that the perpendicular from the centre of a circle to a chord bisects the chord.
$⟹PB=\frac{1}{2}AB=\frac{1}{2}\times 8=4\text{cm}$
Using Pythagoras' theorem in $△OPB,$ we have
$O{B}^2=O{P}^2+P{B}^2.$
$⟹O{P}^2=O{B}^2-P{B}^2$
$=5^2-4^2$
$=25-16$
$=9$
$⟹OP=3\text{cm}$
Thus, the midpoint of the chord is 3 cm away from the centre of the circle.