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555-605 (Medium)|   Geometry|      
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Bunuel
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If the radius of the circle pictured above is 1, what is the measure 06 Mar 2017, 01:52
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35% (medium)

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66% (01:37) correct 34% (01:31) wrong based on 211 sessions

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If the radius of the circle pictured above is 1, what is the measure of minor arc AB?

A. π/9

B. π/6

C. 2π/9

D. 2π/3

E. π

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C
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If the radius of the circle pictured above is 1, what is the measure Updated on: 06 Mar 2017, 20:07
Originally posted by saswata4s on 06 Mar 2017, 03:28.
Last edited by saswata4s on 06 Mar 2017, 20:07, edited 1 time in total.
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Assuming the line passing through A is the diameter:

The vertically opposite angle of 20 degree angle is the same = 20 degree.
If a line is drawn from the center to point B, the angle it will create in the center = 2 * (20) = 40 degree.

Now, the circumference of the circle = 2π*r = 2π.

Therefore, the length of the arc = 40/360 * (2π) = 2π/9.
Answer C.
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If the radius of the circle pictured above is 1, what is the measure 06 Mar 2017, 13:03
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saswata4s
Assuming the line passing through A is the diameter:

The vertically opposite angle of 20 degree angle is the same = 20 degree.
If a line is drawn from the center to point B, the angle it will create in the center = 2 * (20) = 40 degree.

Now, the area of the circle = π*r^2 = π(1)^2 = π.

Therefore, the length of the arc = 40/360 * (π) = π/9.
Answer E.
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Since we're looking for the length of the arc, shouldn't we be using the circumference and not the area?
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If the radius of the circle pictured above is 1, what is the measure 06 Mar 2017, 19:26
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tetriez7
saswata4s
Assuming the line passing through A is the diameter:

The vertically opposite angle of 20 degree angle is the same = 20 degree.
If a line is drawn from the center to point B, the angle it will create in the center = 2 * (20) = 40 degree.

Now, the area of the circle = π*r^2 = π(1)^2 = π.

Therefore, the length of the arc = 40/360 * (π) = π/9.
Answer E.


Since we're looking for the length of the arc, shouldn't we be using the circumference and not the area?
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tetriez7

YOu are right

we should find circumference here ...

2*π*1* 40/360= 2π/9

Ans C
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If the radius of the circle pictured above is 1, what is the measure 06 Mar 2017, 20:09
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tetriez7


Since we're looking for the length of the arc, shouldn't we be using the circumference and not the area?
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You're right. my bad. I corrected in the original reply. Thanks for pointing out.

Cheers.
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If the radius of the circle pictured above is 1, what is the measure 06 Mar 2017, 23:22
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Bunuel

If the radius of the circle pictured above is 1, what is the measure of minor arc AB?

A. \(\frac{π}{9}\)

B. \(\frac{π}{6}\)

C. \(\frac{2π}{9}\)

D. \(\frac{2π}{3}\)

E. \(π\)

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Official solution from Veritas Prep.

If the radius of the circle is 1, then the Circumference is \(2πr\) or \(2π\). If the external angle of the intersecting lines is 20 degrees, then the inside angle is also 20. The angle on the opposite side of the circle is twice the inscribed angle, or 40 degrees. The proportion of the Arc AB is \(\frac{40}{360}\) or \(\frac{1}{9}\). Combining that with the Circumference, the correct answer is \(\frac{2π}{9}\).
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If the radius of the circle pictured above is 1, what is the measure 12 Mar 2017, 15:56
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I now understand the inscribed angle technique and the formula- but logically and mathematically speaking why can we not use 20 in the arc length formula? Visually, it seems to make sense that 20 corresponds to minor arc ab? What is the explanation?
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If the radius of the circle pictured above is 1, what is the measure 12 Mar 2017, 19:22
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Nunuboy1994
I now understand the inscribed angle technique and the formula- but logically and mathematically speaking why can we not use 20 in the arc length formula? Visually, it seems to make sense that 20 corresponds to minor arc ab? What is the explanation?
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Area/length of sector is always calculated from the centre of circle..
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If the radius of the circle pictured above is 1, what is the measure 21 Oct 2022, 05:56
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This question is only solvable if we assume that the line which has point A on it passes through the centre of the circle. This should have been mentioned in the question.
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If the radius of the circle pictured above is 1, what is the measure 02 Nov 2025, 09:57
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