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# In the figure shown, AB is a diameter of the circle and O is the cente

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Math Expert
Joined: 02 Sep 2009
Posts: 53066
In the figure shown, AB is a diameter of the circle and O is the cente  [#permalink]

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15 Oct 2018, 07:00
00:00

Difficulty:

15% (low)

Question Stats:

96% (00:45) correct 4% (02:28) wrong based on 35 sessions

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In the figure shown, AB is a diameter of the circle and O is the center of the circle. If A = (3, 4), then what is the circumference of the circle?

(A) 33

(B) 44

(C) 4π

(D) 5π

(E) 10π

Attachment:

circle.jpg [ 22.41 KiB | Viewed 332 times ]

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In the figure shown, AB is a diameter of the circle and O is the cente  [#permalink]

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15 Oct 2018, 07:05
Distance between points O(0,0) & A(3,4) = $$\sqrt{{(0-3)^2 + (0-4)^2}}= 5$$ = radius of the circle(r).
Circumference = 2r*pi= 10pi ........ Ans E
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Re: In the figure shown, AB is a diameter of the circle and O is the cente  [#permalink]

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15 Oct 2018, 08:08
Bunuel wrote:

In the figure shown, AB is a diameter of the circle and O is the center of the circle. If A = (3, 4), then what is the circumference of the circle?

(A) 33

(B) 44

(C) 4π

(D) 5π

(E) 10π

Attachment:
circle.jpg

General equation of a circle = $$(X_2 - X_1)^2 + (Y_2 - Y_1)^2 = r^2$$

Given we know that the radius is from the origin the equation then can be in this form $$(X)^2 + (Y)^2 = r^2$$

As a result we know $$(3)^2 + (4)^2 = 25$$

$$r^2 = 25$$

$$r = 5$$

Circumference = $$2*pi*r = 2*pi*5 = 10pi$$

Re: In the figure shown, AB is a diameter of the circle and O is the cente   [#permalink] 15 Oct 2018, 08:08
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