Question

if the length of the chord which is at a perpendicular distance of 7 cm from the centre is 48 CM then the radius of the circle is​

Answer 1

Length of chord = 48 cm

Perpendicular distance from the centre = 7 cm

We know that, the perpendicular drawn from the centre of a circle to a chord bisects the chord

So, MB = AB/2

MB = 48/2

MB = 24 cm

Consider ΔOMB

Since OM is perpendicular to AB

ΔOMB is a right - angled triangle

Base = 24 cm

Radius of the circle be Hypotenuse

Height = 7 cm

In right - angled triangle,

By Pythagoras theorem,

Hypotenuse² = Base² + Height²

Hypotenuse² = 24² + 7²

Hypotenuse² = 576 + 49

Hypotenuse² = 625

Hypotenuse = √625

Hypotenuse = 25

So, Hypotenuse = Radius = 25 cm

∴ Radius of the circle is 25 cm.