Question

If radii of two concentric circles are 3 cm and 4 cm, then find the

length of each chord of one circle which is tangent to the other circle.​

Answer 1

Answer:

Correct option is

B

6 cm

Given−

TheradiioftwoconcentriccirleswithcentreOare5cm&4cm.

ThechordABofoutercircletouchestheinnercircleatP.

Tofindout−

ThelengthofAB=?.

The radius of a circle is at the right angle at the point of contact of the tangent to the circle with the tangent.

Solution−

ABtouchestheinnercircleatP.

∴AB=2AP,OP⊥AB

⟹ΔAOPisarightangledonewithAOasthehypotenuse.

NowinΔAOPAO=5CM,OP=4cm

∴AP=

AO

2

−AP

2

=

5

2

−4

2

cm=3cm.

∴AB=2AP=2×3cm=6cm

Ans−OptionB