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# In the circle with center O above, PS = 8. If x = 75, then what is the

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Math Expert
Joined: 02 Sep 2009
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In the circle with center O above, PS = 8. If x = 75, then what is the  [#permalink]

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20 Jul 2018, 00:22
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35% (medium)

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78% (02:38) correct 22% (03:08) wrong based on 42 sessions

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In the circle with center O above, PS = 8. If x = 75, then what is the perimeter of the shaded region?

A. 6- 2 √3
B. 2π/3
C. 2π/3 + 8
D. 2π/3 - 2√3 + 6
E. 2π/3 + 2√3 + 6

Attachment:

2018-07-20_1119.png [ 15.75 KiB | Viewed 890 times ]

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Location: India
Concentration: Finance, Marketing
Schools: CUHK '21 (II)
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Re: In the circle with center O above, PS = 8. If x = 75, then what is the  [#permalink]

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20 Jul 2018, 01:09
1

just use right angle triangle property with angles $$90^{\circ}$$, $$60^{\circ}$$, $$30^{\circ}$$
sides will be in ratio = 2 : $$\sqrt{3}$$: 1
we know radius = 4 also hypotenuse

so other sides can be found out and as we know sector angle = $$30^{\circ}$$
we can find sector circumference.
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Re: In the circle with center O above, PS = 8. If x = 75, then what is the  [#permalink]

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20 Jul 2018, 01:09
Bunuel wrote:

In the circle with center O above, PS = 8. If x = 75, then what is the perimeter of the shaded region?

A. 6- 2 √3
B. 2π/3
C. 2π/3 + 8
D. 2π/3 - 2√3 + 6
E. 2π/3 + 2√3 + 6

Attachment:
2018-07-20_1119.png

OA:D

In 30-60-90 triangle , sides are in ratio of $$a:\sqrt{3}a:2a$$.
$$2a=radius=4, a=2$$
Other sides of triangle are $$2, 2\sqrt{3}$$

Perimeter of shaded area = $$2*\pi*4*\frac{30}{360}+2+(4-2\sqrt{3})$$
=$$\frac{{2\pi}}{3}+6-2\sqrt{3}$$
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Joined: 03 Feb 2016
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In the circle with center O above, PS = 8. If x = 75, then what is the  [#permalink]

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20 Jul 2018, 09:22
Bunuel wrote:

In the circle with center O above, PS = 8. If x = 75, then what is the perimeter of the shaded region?

A. 6- 2 √3
B. 2π/3
C. 2π/3 + 8
D. 2π/3 - 2√3 + 6
E. 2π/3 + 2√3 + 6

Attachment:
2018-07-20_1119.png

QS=2 (30-60-90)
OS= 2√3
QR= 30/360 (2*π*4)=2π/3
SO PERIMETER,
Option D. 2π/3 - 2√3 + 6
In the circle with center O above, PS = 8. If x = 75, then what is the   [#permalink] 20 Jul 2018, 09:22
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