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24 Jul 2019, 01:34
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B
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:
74% (01:44) correct
26%
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wrong
based on 209
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Properties of circles - Practice Question #2
In the diagram given above, O is the center of the circle. If OB = 5 cm and ∠ABC = 30 degree then what the length of the arc AC?
A. \(\frac{5 π}{6}\)
B. \(\frac{5 π}{3}\)
C. \(\frac{5 π}{2}\)
D. 5 π
E. 10 π
To read the article: Properties of circles
To read all our articles:Must Read articles to reach Q51
In the diagram given above, O is the center of the circle. If OB = 5 cm and ∠ABC = 30 degree then what the length of the arc AC?
A. \(\frac{5 π}{6}\)
B. \(\frac{5 π}{3}\)
C. \(\frac{5 π}{2}\)
D. 5 π
E. 10 π
To read the article: Properties of circles
To read all our articles:Must Read articles to reach Q51
saurabh9gupta
Joined: 10 Jan 2013
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24 Jul 2019, 02:11
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So here the angle ACB is 90 degree coz AB is the diameter. Therefore angle CAO becomes 60 degree.
Since OA and OC are radius.. therefore CAO becomes an equilateral triangle.
Arc AC is
(Theta/360)× 2 × pi × r
Theta is 60 degree
R is 5
Answer B
Posted from my mobile device
Since OA and OC are radius.. therefore CAO becomes an equilateral triangle.
Arc AC is
(Theta/360)× 2 × pi × r
Theta is 60 degree
R is 5
Answer B
Posted from my mobile device
24 Jul 2019, 02:15
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To solve this question, let us first derive all possible information from the figure.
Since OB=5 cm is the radius, we can deduce that OA=OC=5cm.
In triangle OBC, OB=OC=5cm, which proves that this is an isosceles triangle. Angles opposite to equal sides in a triangle are also equal. Thus, angle OBC= angle OCB= 30 degrees. This implies that the remaining angle COB= 180- (30+30)=120 degrees since sum of all angles of a triangle equal 180 degrees.
Since AB is a straight line (diameter), angle AOC= 180-120=60 degrees (sum of angles on a straight line equal 180 degrees). Now, to find length of the arc AC, let us first calculate the perimeter of the full circle, which is 2\(π\)r=10\(π\). Now we will be dividing the perimeter into arcs based on the angle it forms with the center. For Arc AC, we have calculated that it forms an angle of 60 degrees. Thus, dividing the perimeter by 6 should give us the right answer, which is 10\(π\)/6=5\(π\)/3
Correct answer: B
Since OB=5 cm is the radius, we can deduce that OA=OC=5cm.
In triangle OBC, OB=OC=5cm, which proves that this is an isosceles triangle. Angles opposite to equal sides in a triangle are also equal. Thus, angle OBC= angle OCB= 30 degrees. This implies that the remaining angle COB= 180- (30+30)=120 degrees since sum of all angles of a triangle equal 180 degrees.
Since AB is a straight line (diameter), angle AOC= 180-120=60 degrees (sum of angles on a straight line equal 180 degrees). Now, to find length of the arc AC, let us first calculate the perimeter of the full circle, which is 2\(π\)r=10\(π\). Now we will be dividing the perimeter into arcs based on the angle it forms with the center. For Arc AC, we have calculated that it forms an angle of 60 degrees. Thus, dividing the perimeter by 6 should give us the right answer, which is 10\(π\)/6=5\(π\)/3
Correct answer: B
