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Circle P shown above is centered at P. If the length of arc ABC is 40,

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Circle P shown above is centered at P. If the length of arc ABC is 40,  [#permalink]

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09 May 2015, 05:14
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Difficulty:

35% (medium)

Question Stats:

71% (01:49) correct 29% (01:14) wrong based on 80 sessions

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Circle P shown above is centered at P. If the length of arc ABC is 40, what is the area of circle P?

A. $$\frac{10'000}{\pi^{2}}$$
B. $$\frac{10'000}{\pi}$$
C. 10'000
D. 10'000$$\pi$$
E. 10'000 $$\pi^{2}$$
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Re: Circle P shown above is centered at P. If the length of arc ABC is 40,  [#permalink]

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09 May 2015, 05:35
$$\frac{72}{360}$$ * 2 * π * PC = 40

PC = $$\frac{100}{π}$$
Area of circle = π * $$(\frac{100}{π})^2$$ = $$\frac{10,000}{π}$$
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Circle P shown above is centered at P. If the length of arc ABC is 40,  [#permalink]

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13 Jul 2015, 12:41
ritigl wrote:
$$\frac{72}{360}$$ * 2 * π * PC = 40

PC = $$\frac{100}{π}$$
Area of circle = π * $$(\frac{100}{π})^2$$ = $$\frac{10,000}{π}$$

Edited

But now I don't understand Area of circle = π * $$(\frac{100}{π})^2$$ = $$\frac{10,000}{π}$$

how do we lose the second pi

we get 10,000 in the numerator (100*100) then pi^2 in the denominator. Does the pi then.... oh wait I just answered my second question... haha
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Circle P shown above is centered at P. If the length of arc ABC is 40,  [#permalink]

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Updated on: 13 Jul 2015, 13:00
1
DropBear wrote:
ritigl wrote:
$$\frac{72}{360}$$ * 2 * π * PC = 40

PC = $$\frac{100}{π}$$
Area of circle = π * $$(\frac{100}{π})^2$$ = $$\frac{10,000}{π}$$

Edited

But now I don't understand Area of circle = π * $$(\frac{100}{π})^2$$ = $$\frac{10,000}{π}$$

how do we lose the second pi

The last step is :π * $$(\frac{100}{π})^2$$ =$$\pi$$ * $$\frac{100^2}{\pi^2}$$ =$$\pi$$ * $$\frac{10000}{\pi^2}$$ -----> you cancel out the $$\pi$$ from the numerator and from the denominator to get $$10000/\pi$$

Originally posted by ENGRTOMBA2018 on 13 Jul 2015, 12:55.
Last edited by ENGRTOMBA2018 on 13 Jul 2015, 13:00, edited 3 times in total.
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Re: Circle P shown above is centered at P. If the length of arc ABC is 40,  [#permalink]

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13 Jul 2015, 12:57
Engr2012 wrote:
DropBear wrote:
ritigl wrote:
$$\frac{72}{360}$$ * 2 * π * PC = 40

PC = $$\frac{100}{π}$$
Area of circle = π * $$(\frac{100}{π})^2$$ = $$\frac{10,000}{π}$$

Edited

But now I don't understand Area of circle = π * $$(\frac{100}{π})^2$$ = $$\frac{10,000}{π}$$

how do we lose the second pi

The last step is : $$\frac{10000}{\pi^2}$$ * $$\pi$$ -----> you cancel out the $$\pi$$ from the numerator and 1 from the denominator to get $$10000/\pi$$

Thanks for the clarification. Much appreciated!
Re: Circle P shown above is centered at P. If the length of arc ABC is 40,   [#permalink] 13 Jul 2015, 12:57
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