Question

find the length of a chord which is at a distance of 6 cm from the center of circle whose radius is 10 cm

Answer 1

Given :-

• Distance = 6 cm
• Radius = 10 cm

To Find :-

Length of chord

Solution :-

Let the center of the circle be O
The radius be OA

Distance of chord be OC

The length of chord be AB such that AB = 2AC

Now

In ΔOAC

By using pythagoras theorem

$\sf\leadsto OA^2=OC^2+AC^2$

We have

OA = 10 cm

OC = 6 cm

AC = ?

$\sf\leadsto (10)^2=(6)^2+(AC)^2$

$\sf\leadsto 100=36+(AC)^2$

$\sf\leadsto 100-36=(AC)^2$

$\sf\leadsto 64 = AC^2$

$\sf\leadsto \sqrt{64}=AC$

$\sf\leadsto 8=AC$

Now

$\sf\leadsto AB=2AC$

$\sf\leadsto AB=2(8)$

${\boxed{\underline{\purple{\frak{\leadsto AB=16\;cm}}}}}\bigstar$

Therefore

Length of chord is 16 cm