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monitta
3 years ago
14

Which of the following statements is always true about similar polygons

Mathematics
1 answer:
Ganezh [65]3 years ago
3 0
The correct answer is D. Since the polygons are /similar/ and not /congruent/, C is not necessarily true.

Hope this helps.
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✨ B R A I N L I E S T
miv72 [106K]

1

:x

2

+y

2

−6x−9y+13=0

(x−3)

2

+(y−

2

9

)

2

−9−

4

81

+13=0

(x−3)

2

+(y−

2

9

)

2

=

4

65

Here,

r

1

=

2

65

C

1

=(3,

2

9

)

Equation of another circle-

S

2

:x

2

+y

2

−2x−16y=0

(x−1)

2

+(y−8)

2

−1−64=0

(x−1)

2

+(y−8)

2

=65

Here,

r

2

=

65

C

2

=(1,8)

Distance between the centre of two circles-

C

1

C

2

=

(3−1)

2

+(8−

2

9

)

2

C

1

C

2

=

4+

4

49

=

2

65

∣r

2

−r

1

∣=

∣

∣

∣

∣

∣

∣

65

−

2

65

∣

∣

∣

∣

∣

∣

=

2

65

∵C

1

C

2

=∣r

1

−r

2

∣

Thus the two circles touches each other internally.

Since the circle touches each other internally. The point of contact P divides C

1

C

2

externally in the ratio r

1

:r

2

, i.e.,

2

65

:

65

=1:2

Therefore, coordinates of P are-

⎝

⎜

⎜

⎜

⎜

⎜

⎛

1−2

1(1)−2(3)

,

1−2

1(8)−2(

2

9

)

⎠

⎟

⎟

⎟

⎟

⎟

⎞

=(5,1)

Therefore,

Equation of common tangent is-

S

1

−S

2

=0

(5x+y−6(

2

x+5

)−9(

2

y+1

)+13)−(5x+y−2(

2

x+5

)−16(

2

y+1

))=0

2

−6x−9y−13

+x+8y+13=0

4x−7y−13=0

Hence the point of contact is (5,1) and the equation of common tangent is 4x−7y−13=0.

4 0
2 years ago
Read 2 more answers
Y is directly proportional to x<br> when y=30, x=6
daser333 [38]

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y = 5x

❤❤❤❤❤❤❤❤❤❤❤❤❤

8 0
2 years ago
Read 2 more answers
Circumfrance of a circle, (Show working)
Ronch [10]

Answer:

25.1cm

Step-by-step explanation:

C=2πr

here radius, r=4 cm and π=3.142

Put values in formula.

C=2(3.142)(4)

C=25.1 cm (Rounded to 1 decimal place)

3 0
2 years ago
Read 2 more answers
The ratio of Aspens to Ponderosa Pines in a part of a forest is 12 to 16. If there are 12 Ponderosa Pines, how many Aspens are t
Romashka-Z-Leto [24]
Is this the same question from the other one.
8 0
2 years ago
Karrem says that the ratio 4:1 is eqivilent to the ratio of 12:9 because 4+8=12 and 1+8 =9 is karreem correct
Mariana [72]

Answer:

No, Kareem is incorrect.

Step-by-step explanation:

Kareem says that the ratio of \frac{4}{1}=\frac{12}{9} because 4 + 8 = 12 and 1 + 8 = 9

But the correct way to rewrite the ratio 4 : 1 is,

\frac{4}{1}=\frac{4\times 3}{1\times 3}

Which becomes as,

\frac{4}{1}=\frac{12}{3}

Therefore, Kareem is not correct.

Correct ratio equivalent to 4 : 1 is 12 : 3.

8 0
2 years ago
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