Question

two concentric circles are such that chord of the larger circle touches the smaller circle of radius 5cm if the chird is of the length 24cm find the radius of longer circle

Answer 1

Join OQ 
Let us take OM=5cm (radius of the small circle)
                    PQ=24cm(chord of the larger circle)
First we need to prove thier congruency 
In Triangle OMP and Triangle OMQ,
Angle OMP=Angle OMQ (tangents at the point of contact are perpendicular at                                             the point of contact)
OM=OM(common)
OP=OQ(Radii of the larger circle)
Therefore, Triangle OMP=Triangle OMQ
PM=MQ(cpct)
Now, as we now PQ is 24 cm and PM=MQ
we can say PM=12 cm 
By Pythagoras Theorem,
$OP ^{2}$=$OM ^{2}$+$PM ^{2}$
$OP ^{2}$=$5 ^{2}$+$12 ^{2}$
$OP ^{2}$=25+144
$OP ^{2}$=169
OP=$\sqrt{169}$
OP=13 CM


                                    

Answer 2

hope it helps u thq asking me