Question

Distance of chord AB from the centre of a circle is 8 cm. Length of the chord AB is 12 cm. Find the diameter of the circle.

Answer 1

Let the centre of the circle be O.
AB = 12 cm
OC = 8 cm
OC ⊥ AB
We know perpendicular drawn from the centre of the circle to the chord, bisects the chord.
So, AC = 6 cm
In Right angled triangle $\Delta OCA$,
$O{C}^2+A{C}^2=A{O}^2$
$\Rightarrow 8^2+6^2=A{O}^2$
$\Rightarrow A{O}^2=100$
$\Rightarrow AO=10$
Thus, AO = 10 cm
Diameter = 2 × 10 cm = 20 cm.