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30 Nov 2021, 02:30
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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:
78% (01:13) correct
22%
(01:08)
wrong
based on 32
sessions
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Date
Time
Result
Not Attempted Yet
A circle of radius 5, has a chord of length 5√2. What is the angle subtended by the chord at the centre of the circle?
A. 30°
B. 45°
C. 60°
D. 90°
E. 120°
A. 30°
B. 45°
C. 60°
D. 90°
E. 120°
30 Nov 2021, 04:42
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[quote="Bunuel"]A circle of radius 5, has a chord of length 5√2. What is the angle subtended by the chord at the centre of the circle?
A. 30°
B. 45°
C. 60°
D. 90°
E. 120°
[textarea]
Let the chord be AB = 5\sqrt{2}
Let the centre of the circle be O.
Now connect OA and OB to get the triangle OAB.
We need to find the angle AOB or BOA.
We know OA = OB = Radius of the circle
From here we can go for a smart value system.
Smart value system:
Checking the condition for pythogorus: a^2+a^2 = (5\sqrt{2})^2
2a^2 = 25*2
a^2 = 25
a=5
So, we have sides in the ration of 1:1:\sqrt{2}
Which is 45, 45 and 90.
So, central angle will be 90 degrees.
A. 30°
B. 45°
C. 60°
D. 90°
E. 120°
[textarea]
Project PS Butler
Let the chord be AB = 5\sqrt{2}
Let the centre of the circle be O.
Now connect OA and OB to get the triangle OAB.
We need to find the angle AOB or BOA.
We know OA = OB = Radius of the circle
From here we can go for a smart value system.
Smart value system:
Checking the condition for pythogorus: a^2+a^2 = (5\sqrt{2})^2
2a^2 = 25*2
a^2 = 25
a=5
So, we have sides in the ration of 1:1:\sqrt{2}
Which is 45, 45 and 90.
So, central angle will be 90 degrees.
DashingNightmare2
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Joined: 30 May 2021
Last visit: 19 Jun 2022
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GMAT 1: 750 Q50 V41
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30 Nov 2021, 12:13
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Bunuel
In a circle, 2 radius and a chord makes a triangle
Now radius is same i.e 5
and chord length is 5√2, which can be obtained when we do √5^2+5^2, which makes the triangle a right-angled triangle
Hence D
