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06 Oct 2021, 05:00
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A
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Difficulty:
75%
(hard)
Question Stats:
52% (02:23) correct
48%
(02:31)
wrong
based on 114
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Rectangle ABDC is perfectly inscribed inside a circle and has an area of 40 square inches. What is the length of minor arc CD?.
(1) The sum of the measures of angle m and angle n is 60 degrees.
(2) The sum of the measures of angle j and angle n is 90 degrees.
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PyjamaScientist
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06 Oct 2021, 05:48
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Option D looks like the right answer to me.
From the figure, we can ascertain that m = n, and k = j because they are alternate angles of the diagonal inside a rectangle.
Also, it's given that BD * CD = 48 --------- (1)
Statement 1:
m + n = 60\(^{\circ}\)
since m = n, thus m = n = 30\(^{\circ}\)
From this I can get, Tan 30\(^{\circ}\) = \(\frac{BD}{CD}\) = \(\frac{1}{\sqrt{3}}\) ---------(2)
From (1) and (2), we can get the individual values of BD and CD. And thus from the Pythagoras theorem, we can get the value of our Hypotenuse which happens to be our radius as well.
We can similarly find the angle inscribed by the arc CD as we know the other two angels.
Thus the length of the arc CD can be determined as the length of an arc is given by radius * angle. Hence, it is sufficient.
Statement 2: This statement gives us j + n = 90\(^{\circ}\). This gives the same information as statement 1. And since statement 1 is sufficient. This too shall be sufficient.
From the figure, we can ascertain that m = n, and k = j because they are alternate angles of the diagonal inside a rectangle.
Also, it's given that BD * CD = 48 --------- (1)
Statement 1:
m + n = 60\(^{\circ}\)
since m = n, thus m = n = 30\(^{\circ}\)
From this I can get, Tan 30\(^{\circ}\) = \(\frac{BD}{CD}\) = \(\frac{1}{\sqrt{3}}\) ---------(2)
From (1) and (2), we can get the individual values of BD and CD. And thus from the Pythagoras theorem, we can get the value of our Hypotenuse which happens to be our radius as well.
We can similarly find the angle inscribed by the arc CD as we know the other two angels.
Thus the length of the arc CD can be determined as the length of an arc is given by radius * angle. Hence, it is sufficient.
Statement 2: This statement gives us j + n = 90\(^{\circ}\). This gives the same information as statement 1. And since statement 1 is sufficient. This too shall be sufficient.
03 Nov 2021, 06:44
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This question is a part of Are You Up For the Challenge: 700 Level Questions collection.
