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O ​is the center of the circle, and the perimeter of Δ AOB

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O ​is the center of the circle, and the perimeter of Δ AOB [#permalink] New post 21 Jan 2017, 09:09
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Question Stats:

85% (00:31) correct 14% (00:24) wrong based on 28 sessions


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O is the center of the circle, and the perimeter of Δ AOB is 6.

Quantity A
Quantity B
The circumference of the circle
12


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Re: O ​is the center of the circle, and the perimeter of Δ AOB [#permalink] New post 24 Jan 2017, 19:39
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Explanation

In order to find the circumference of the circle, we need the radius, since circumference = 2πr. Both OA and OB are radii of the circle.

Triangle OAB is an equilateral triangle:


If ∠O is 60°, then ∠A + ∠B = 120°, because
∠O + ∠A + ∠B = 180°
60° + ∠A + ∠B = 180°
∠A + ∠B = 120°

∠A and ∠B are equal because triangles that have two vertices on the circle and one at the center of the circle are always isosceles triangle. So 120° ÷ 2 = 60°.

Thus, ∠O is 60°, ∠A is 60°, and ∠B is 60°. Triangle OAB is an equilateral triangle.

The perimeter of triangle ΔOAB is 6. Because each side of an equilateral triangle is of equal length, both OA and OB = 2 (length of 6 ÷ 3 sides = length of 2).

Now find the circumference:

C = 2πr → C = 2π2 → C = 4π → C = 4 × (3.14) → C = 12.56

Compare the quantities:

Quantity A: 12.56
Quantity B: 12


Hence option A is correct.
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Re: O ​is the center of the circle, and the perimeter of Δ AOB   [#permalink] 24 Jan 2017, 19:39
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O ​is the center of the circle, and the perimeter of Δ AOB

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