Question

Two concentric circles are of radii 5 cm and 3 cm. Find the length of the
chord of the larger circle (in cm) which touches the smaller circle.
[CBSE 2012, '14)​

Answer 1

Answer:

first lets recall a few things

the tangent at any point of a circle is perpendicular to the radius through the point of contact.    (1)

the perpendicular from the center of the  chord bisects the chord. (2)        

plzz refer to the attachment also.      

let O be the center common to the two circles . join OM and OP    

PQ is the chord of the larger circle (in cm) which touches the smaller circle.

then,

by (1)

ΔOMP is right angled so

OP²=OM²+PM² pythagoras ofcourse

5²=3²+PM²

PM²=5²-3²=16

then PM=√16=4

now by (2)

PM=MQ=4

so PM+MG=PQ=4+4=8cm

hope this helps...