AD is the diameter of a circle and AB is a chord If AD 34 cm AB 30 cm the distance of AB from the ce...........

Quantitative Aptitude (CDS) Mensuration 2D

AD is the diameter of a circle and AB is a chord. If AD = 34 cm, AB = 30 cm, the distance of AB from the centre of the circle is

17 cm

15 cm

13 cm

8 cm

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Explanation:

Let O be the centre of the circle.
Draw OC ⊥ AB.
OC is the distance of the chord ABfrom the centre of the circle.
OB = Radius of the circle = 17 cm
BC=AC=30/2=15cm
(Perpendicular from the centre to the chord bisects the chord)
In ΔABC,
OC= $\sqrt{OB^{2}-BC^{2}}=\sqrt{17^{2}-15^{2}}$
$=\sqrt{289-225}=\sqrt{64}= \;8cm$