Question

Radius of a circle is 5cm . Distance of a chord from the centre of the circle is 3cm. then what is the length of chord
​

Answer 1

Explanation:

construct a line from the centre to one of the end of chord which is the radius = 5cm which becomes the hypotenuse

which makes a right angled triangle the the perpendicular = distance of the chord from the centre = 3cm

by using Pythagoras theorem

${hypotenuse}^{2} = {base}^{2} + {perpendicular}^{2}$

${5}^{2} = {base}^{2} + {3}^{2}$

$25 - 9 = {base}^{2}$

$16 = {base}^{2}$

$\sqrt{16} = base$

$4 = base$

length of the chord = base *2

=4*2

=8cm

Answer 2

${\textsf{\textbf{\underline{\underline{The length of the chord of distance 3cm from its centre is 8cm.</p><p>\::}}}}}$

Step-by-step explanation:

Given that,

• Radius of a circle is 5cm .
• Distance of a chord from the centre of the circle is 3cm.

To find,

• what is the length of chord

formulas used,

• Pythagoras theorem

solusions,

• Given radius of the circle (AC) = 5 cm  
• AO =3 cm

Consider the triangle AOC, which is a right angled triangle.

By applying Pythagoras theorem, we can write,

$\begin{array}{l}{\mathrm{AO}^{2}+\mathrm{OC}^{2}=\mathrm{AC}^{2}} \\ {3^{2}+\mathrm{OC}^{2}=5^{2}} \\ {9+\mathrm{OC}^{2}=25} \\ {\mathrm{OC}^{2}=16}\end{array}$

Taking square root,  

OC = 4,

${\textsf{\textbf{\underline{\underline{∴ Therefore the length of the chord = 4 + 4 = 8 cm.\::}}}}}$