Question

The distance of chord AB from the centre of a circle is 8 cm. The length of the chord AB is 12 cm. Find the diameter of a circle

Answer 1

Given: In a circle with centre O,
OA is radius and AB is its chord, seg OP ⊥ chord AB

AB = 12 cm and OP =8 cm

To Find: Diameter of the circle

$AP=\frac{1}{2}$ AB (Perpendicular drawn from the
centre of a circle to the chord bisects the chord)

$\therefore AP=\frac{1}{2}\times 12=6cm$ ….(i)

In $\Delta OPA,\angle OPA={90}^o$

$O{A}^2=O{P}^2+A{P}^2$ (Pythagoras theorem)

$=8^2+6^2$

$=64+36$

$O{A}^2=100$

$O{A}^2=\sqrt{100}=10$ cm

Radius (r) = 10 cm

Thus, diameter = 2r = 2 $\times$ 10 = 20 cm