Question

a chord of length 16 cm is drawn in a circle of radius 10 cm find the distance of the chord from the centre of the circle​

Answer 1

★Given:-

• Length of chord= 16cm
• Radius of circle = 10cm

★To find:-

• Distance of the chord from the centre of the circle.

★Solution:-

We know,

✦A Perpendicular drawn from the centre of the circle to the chord ,bisects the chord.Hence,the point will be the mid point of the line segment.

Refer to the attachment for diagram

From the diagram,

Radius = OA = 10cm

Chord = AB = 16cm

C = Midpoint of AB

Hence,

=>AC = AB / 2

         = 16 / 2

          = 8cm.

We know:

By Pythagoras theorem:-

$\leadsto \underline{\boxed{\sf (Hypotenuse)^2=(opposite\ side)^2+(adjacent\ side )^2 }}$

From ΔAOC ,

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

We have

• OA = 10cm
• AC = 8cm
• OC = ?

Substituting these values,

$\mapsto \sf OA^2 = OC^2 + AC^2\\\\\mapsto \sf 10^2 = OC^2 + 8^2\\\\\mapsto \sf 100 = OC^2 + 64\\\\\mapsto \sf OC^2 = 36\\\\\mapsto \underline{\boxed{\bold{OC = 6cm.}}}$

Hence,

The distance of the chord from the centre of the circle is 6cm.

________________

Answer 2

Answer:

$\huge\rm{Solution:–} \\ \\ \rm→10²=x²+8² \\ \rm→100-84=x² \\ \rm→36=x²=6² \\ \rm \: Answer→x=6 \\ \rm{distance} = 6cm$