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14 Jul 2020, 01:53
Kudos
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D
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:
70% (01:34) correct
30%
(01:50)
wrong
based on 57
sessions
History
Date
Time
Result
Not Attempted Yet
A chord AB of a circle subtends an angle of 120° at the centre O. If the radius of the circle is 2. What is the area of the triangle AOB?
A. 1
B. √3/2
C. √2
D. √3
E. Cannot be determined
A. 1
B. √3/2
C. √2
D. √3
E. Cannot be determined
Attachments
circle.png [ 3.57 KiB | Viewed 4359 times ]
14 Jul 2020, 02:41
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IMO D
The chord creates an isosceles triangle. With OA = OB = 2
A perpendicular to the chord from AB (Height of triangle) makes two 30 - 60 - 90 triangle with 90 degree angle opposite to one of the sides .
The sides of triangle are (a : a * Sqrt(3) :2a) >> (1 : 1 *Sqrt(3) :2)
So length of chord AB = 2* Sqrt(3)
Area of triangle = 1/2 * 2*Sqrt(3) * 1 ====> sqrt (3)
Ans: D
The chord creates an isosceles triangle. With OA = OB = 2
A perpendicular to the chord from AB (Height of triangle) makes two 30 - 60 - 90 triangle with 90 degree angle opposite to one of the sides .
The sides of triangle are (a : a * Sqrt(3) :2a) >> (1 : 1 *Sqrt(3) :2)
So length of chord AB = 2* Sqrt(3)
Area of triangle = 1/2 * 2*Sqrt(3) * 1 ====> sqrt (3)
Ans: D
Attachments
chord AB.jpg [ 2.19 MiB | Viewed 4300 times ]
