Question

Two chords AB and CD of a circle are each at distance 4 cm from the centre . If AB =5 cm then find the length of CD?​

Answer 1

Given- AB&CD are chords of a circle and they are equidistant (4cm) from the centre O.

To find out- Whether AB=CD.

Solution-

OM and ON are perpendiculars=4cm from O to AB & CD, respectively.

∴ They bisect AB & CD

i.e AM=

2

1

AB & DN=

2

1

DC

∠OMA=∠OND=90

o

.

Now, between the ΔAOM & △DON we have, OM=ON=4cm ...(given),

∠OMA=∠OND=90

o

OA=OD ...(radii of the same circle).

∴ΔAOM≡ΔDON ...(RHS test).

∴AM=DN⟹AB=DC.

So, the statement is true.