Question

If the length of the chord of a circle is 8 cm and it is at a distance of 3 cm from the centre of
the circle, then find the radius of the circle,​

Answer 1

Answer

Here ,

let O be the centre of the circle

AB be the chord

AB = 8 cm

OM perpendicular to AB

[ since the shortest distance from a point to a line is the perpendicular ]

OM = 3cm

MB = 1/2AB [since perpendicular from

the bisects the chord ]

i.e.MB = 4 cm

then , in rt. triangle OMB

By using pythagoras theorem

(OB)sq. = (OM)sq. + (MB)sq.

(OB)sq. = (3)sq. + (4)sq.

OB = sq. root over 9+16

OB = sq. root 25

OB = 5 cm

hence , radius of the circle = 5cm

hope it helps