Question

3 geometry questions, 30 points!

Answer 1

○
`\displaystyle 4,08\:cm.`

○
`\displaystyle 8,3`

Step-by-step explanation:

`\displaystyle √([CB]^2 + [BA]^2) = d → √(0,5^2 + 1,2^2) = d \\ \\ √(0,25 + 1,44) = d → √(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 (25)/(3) = (3x)/(3) \\ \\ 8(1)/(3) = x \\ \\ 8(1)/(3) ≈ 8,3`

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Answer 2

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

Explanation:

Given two figures :

For Figure first

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 =
`(25)/(3)` = 8.33

For figure second

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 =
`√(1.44+0.25)}`

Or, The Length of diameter of circle AC =
`√(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