Question

Two concentric circles of diameter 30 cm and 18cm find the length of the chord of the larger circle that touches the smaller circle

Answer 1

Solution :-

Given, Two concentric circles of diameters D = 30 cm and d = 18cm ,

First big circule :-

D = 30 cm. then

R = 30÷2 = 15 cm

R = 15 cm

And

Second small circle

d = 18 cm. then

r = 18÷2 = 9 cm

r = 9 cm

Now,

Chord = 2 × ( 2R - 2r )

Chord = 2 × [ 2(15) - 2(9) ]

Chord = 2 × ( 30 - 18 )

Chord = 2 × 12

Chord = 24 cm Answer

Answer 2

Here is a way to solve this using basic trigonometry (refer to the attached illustration):

Line AB's length is equal to the radius of the bigger circle, 15 cm (the problem gives the diameter. half it).

Line AC's length is equal to the radius of the smaller circle, 9 cm (the problem gives the diameter. half it).

Line BD is just one of the infinite number of chords that touches the smaller circle at one point only. We choose this one as it makes solving the problem much more intuitive.

ABC is a right triangle, since line BD (the chord of our choice) is perpendicular to line AC.

We can't compute the length of BD directly, but we can compute the length of line BC which is half the length of BD.

So, using the Pythagorean theorem:

(length of BC)^2 + (length of AC)^2 = (length of AB)^2

Rearranging the formula to suit our problem (note "sqrt" refers to the "square root"):

length of BC  = sqrt[ (length of AB)^2 - (length of AC)^2 ]

length of BC  = sqrt[ 15^2 - 9^2 ]

length of BC = sqrt(225 - 81)

length of BC = sqrt(144)

length of BC = 12 cm

Since the length of BC is half of the length of our chord, line BD, the length of the chord is 24 cm.