Question

A chord of length 6cm is drawn in a circle of radius 5cm. Calculate its distance from the centre of the circle.

Answer 1

See the attached file

Answer 2

Answer:

4 cm

Step-by-step explanation:

Refer the attached figure

Length of Chord AB = 6 cm

Perpendicular Line form the center of the circle to the chord = OC

OB = OA = Radius of circle = 5 cm

Theorem : A perpendicular dropped from the center of the circle to a chord bisects it. It means that both the halves of the chords are equal in length.

So, OB bisects AB

So, $AC = CB =\frac{AB}{2} =\frac{6}{2} =3$

In ΔOCB

$Hypotenuse^2=Perpendicular^2+Base^2$

$OB^2=OC^2+CB^2$

$5^2=OC^2+3^2$

$25=OC^2+9$

$25-9=OC^2$

$16=OC^2$

$\sqrt{16}=OC$

$4=OC$

Hence distance of chord from the center of the circle is 4 cm.