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Anna [14]
2 years ago
14

3 geometry questions, 30 points!

Mathematics
2 answers:
polet [3.4K]2 years ago
8 0

Answer:

A ) The value of x for  the given circle with chords and center is 8.3

B) The circumference of circle with chords 1.2 cm and 0.5 cm is 4.082

Step-by-step explanation:

Given two figures :

<u>For Figure first  </u>

A circle with center y ,  having two chords FM and NM

FM = 5 x

MN = 2 x + 25

Now from theorem of circle ,

Chords equidistant from center of circle are equal in length

I.e distance of chord MN from center y  and distance of FM from center y are equal

So, FM = MN

Or, 5 x = 2 x + 25

Or, 5 x - 2 x = 25

Or, 3 x = 25

∴       x = \frac{25}{3} = 8.33

<u>For figure second</u>

The length of two adjacent chords of circle is 1.2 cm and 0.5 cm

Let the center of circle = O

Length of chord AB = 1.2 cm

Length of chord BC = 0.5 cm

As both chords are at 90° to each other

So The Length of diameter of circle AC = \sqrt{AB^{2}+BC^{2}}

Or, The Length of diameter of circle AC = \sqrt{1.2^{2}+0.5^{2}}

Or, The Length of diameter of circle AC = \sqrt{1.44+0.25}}

Or, The Length of diameter of circle AC = \sqrt{1.69}

∴ The Length of diameter of circle AC = 1.3 cm

So, Circumference of circle = \pi d

Or, Circumference of circle = 3.14 × 1.3

∴ Circumference of circle = 4.082 cm

Hence,

A ) The value of x for  the given circle with chords and center is 8.3

B) The circumference of circle with chords 1.2 cm and 0.5 cm is 4.082 Answer

Black_prince [1.1K]2 years ago
6 0

Answer:

○ \displaystyle 4,08\:cm.

○ \displaystyle 8,3

Step-by-step explanation:

\displaystyle \sqrt{[CB]^2 + [BA]^2} = d → \sqrt{0,5^2 + 1,2^2} = d \\ \\ \sqrt{0,25 + 1,44} = d → \sqrt{1,69} = d → 1,3 = d \\ \\

Now use the diameter in the circumference formula:

\displaystyle 2πr = C\:or\:πd = C \\ \\ 1,3π ≈ 4,08407045 ≈ 4,08

Two equidistant chords are congruent, therefore the two segments are congruent, so you would set them equal to each other:

2x + 25 = 5x

- 2x - 2x

___________

\displaystyle \frac{25}{3} = \frac{3x}{3} \\ \\ 8\frac{1}{3} = x \\ \\ 8\frac{1}{3} ≈ 8,3

I am joyous to assist you anytime.

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