Question

In figure, if OA = 5 cm, AB = 8 cm and OD is perpendicular to AB, then CD is equal to ___.

• A. 1 cm
• B. 3 cm
• C. 2 cm
• D. 5 cm

Answer 1

The correct option is C 2 cm

We know that the perpendicular from the centre of a circle to a chord bisects the chord.
$⟹AC=CB=\frac{1}{2}AB=\frac{1}{2}\times 8=4cm$
Given that OA= 5 cm.
Using Pythagoras' theorem in $△OAC,$
$A{O}^2=A{C}^2+O{C}^2.$
i.e., $5^2=4^2+O{C}^2$
$⟹O{C}^2=25-16=9$
$⟹OC=3cm$
[taking positive square root, because length is always positive]
Note that OA = OD [radii of the same circle]
Also, OD = 5 cm.
$⟹$CD = OD - OC = 5 - 3 = 2 cm