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02 Sep 2018, 22:13
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
78% (01:32) correct
22%
(01:33)
wrong
based on 36
sessions
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What is the measure of arc XYZ, if points X, Y and Z are points that lie, in that order, on a circle O?
(1) Sector XYZO has an area of \(\frac{3\pi}{2}\) and is 1/6 the area of the circle.
(2) The measure of chord XZ is 3.
(1) Sector XYZO has an area of \(\frac{3\pi}{2}\) and is 1/6 the area of the circle.
(2) The measure of chord XZ is 3.
03 Sep 2018, 03:08
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Bunuel
Measure of Any arc = (Angle/360)*2πr
Question : What is the measure of arc XYZ?
i.e. We need
1) Angle drawn by are XYZ at the centre of the circle
2) Radius of the circle
Statement 1: Sector XYZO has an area of \(\frac{3\pi}{2}\) and is 1/6 the area of the circle
i.e. (1/6)πr*2 = \(\frac{3\pi}{2}\)
SO we know the radius
as well as (1/6) = (Angle)/360
i.e. Angle at centre by XYZ = 60º hence
SUFFICIENT
Statement 2: The measure of chord XZ is 3.
NOT SUFFICIENT
Answer: Option A
03 Sep 2018, 03:18
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Bunuel
(1) Sector XYZO has an area of \(\frac{3\pi}{2}\) and is 1/6 the area of the circle.
the angle is 360/6 = 60
\(\pi r^2\)\(\frac{60}{360}\) = \(3\pi\)
this should give us radius followed by measure of arc , which is 2\(\pi\)r
sufficient
(2) The measure of chord XZ is 3.
clearly insufficient
A
