Question

3 geometry questions, 30 points!

Answer 1

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 :

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 = $\frac{25}{3}$ = 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 = $\sqrt{1.44+0.25}}$

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

Answer 2

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

___________

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

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