Question

Question 2
In figure, if OA = 5 cm, AB = 8 cm and OD is perpendicular to AB, then CD is equal to

(A) 2 cm
(B) 3 cm
(C) 4 cm
(D) 5 cm

Answer 1

The answer is (A).
We know that, the perpendicular from the centre of a circle to a chord bisects the chord.
$AC=CB=\frac{1}{2}AB=\frac{1}{2}\times 8=4cmgiven,OA=5cmA{O}^2=A{C}^2+O{C}^2\left[usingpythagorastheorem\right](5{)}^2=(4{)}^2+O{C}^{2}25=16+O{C}^{2}O{C}^2=25-16=9OC=3cm$
[taking positive square root, because length is always positive]
OA = OD [same radius of a circle]
OD = 5 cm
CD = OD - OC = 5 - 3 = 2 cm