Math, asked by nur91, 1 year ago

find the ratio between lengths of two chords distants d1 cm and d2 cm from the centre of a circle of radius r cm

Answers

Answered by angela97
5
Let the lengths of the two chords be x and y
Distance of x from centre=d1
Distance of y from centre =d2
Radius =r
Length of x=2(r-d)
Length of y=2(r-d)
Therefore, X/y=2(r-d)/2(r-d)=1
The ratio is 1:1
Answered by shradhaaa488922
1

Answer:

Let the two concentric circles have the center O and let AB be the chord of an outer circle whose length is D and which is also tangent to the inner circle at point D as shown

The diameters are given as d

1

and d

2

hence the radius will be

2

d

1

and

2

d

2

In Δ OAB

⇒ OA = OB .... radius of the outer circle

Hence Δ OAB is an isosceles triangle

As radius is perpendicular to tangent OD is perpendicular to AB

OD is altitude from the apex and , in an isosceles triangle , the altitude is also the median

Hence AD = DB =

2

c

Consider Δ ODB

⇒∠ ODB = 90

...radius perpendicular to tangent

Using Pythagoras theorem

⇒OD

2

+BD

2

=OB

2

2

2

d

2

2

+

2

2

C

2

=

2

2

d

1

2

Multiply the whole by 2

2

⇒d

2

2

+C

2

=d

1

2

Hence proved

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