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

REF.Image

Sol: Given distance OM=8 cm

Length AB= 12 cm

$OM\perp AB$

To find: Diameter of the circle

$OM\perp AB$

$\therefore AM=\frac{1}{2}AB[\perp$ drawn from center to chord bisect it]

$=\frac{1}{2}.12$

$=6cm$

$\therefore$ In $\Delta AMD$

By Pythagoras theorem

$(AO{)}^2=A{M}^2+M{O}^2$

$A{O}^2=(6{)}^2+(8{)}^2$

$A{O}^2=36+64$

$AO=\sqrt{100}$

$AO=10cm$

$\therefore$ Diameter = $2\times$ radius

$=2\times 10cm$

$=20cm$

$\therefore$ Diameter of the circle = 20 cm.