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TheUltimateWinner
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01 Jul 2020, 02:45
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
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Question Stats:
58% (02:42) correct
42%
(01:44)
wrong
based on 19
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Not Attempted Yet
In the figure below, what is the area of triangle inscribed in the semi-circle drawn in the xy-plane?
A) 6
B) 8
C) 6√2
D) 9
E) 9√2
A) 6
B) 8
C) 6√2
D) 9
E) 9√2
Attachments
figure.PNG [ 8.83 KiB | Viewed 1221 times ]
yashikaaggarwal
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01 Jul 2020, 03:00
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=> 16+H^2 = YX'^2
=> 4+H^2 = YX^2
=> H^2 = YX'^2-16
=> H^2 = YX^2-4
Equating both
YX'^2-16 = YX^2-4
YX'^2-YX^2 = 12 -----------(1)
Also, using Pythagoras theorem,
YX'^2+YX^2 = 36 ----------(2)
Equating both equations,
2YX'^2 = 48
YX'^2 = 24
YX' = √2*2*2*3
YX' = 2√6
And YX = √24-12
YX = √12
YX = 2√3
Arae of triangle = 1/2*2√3*2√6
= √3*2*√3*√2
= 6√2
Answer is C
Posted from my mobile device
=> 4+H^2 = YX^2
=> H^2 = YX'^2-16
=> H^2 = YX^2-4
Equating both
YX'^2-16 = YX^2-4
YX'^2-YX^2 = 12 -----------(1)
Also, using Pythagoras theorem,
YX'^2+YX^2 = 36 ----------(2)
Equating both equations,
2YX'^2 = 48
YX'^2 = 24
YX' = √2*2*2*3
YX' = 2√6
And YX = √24-12
YX = √12
YX = 2√3
Arae of triangle = 1/2*2√3*2√6
= √3*2*√3*√2
= 6√2
Answer is C
Posted from my mobile device
01 Jul 2020, 03:01
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TheUltimateWinner
Property:
- Ant triangle drawn in a semicircle (with two vertices at diameter) makes 90o on circumference
- The hypotenuse of this right triangle = Diameter of Circle
- Ant triangle drawn in a semicircle (with two vertices at diameter) makes 90o on circumference
- The hypotenuse of this right triangle = Diameter of Circle
Diamater of the Circle = Hypotenuse of Right triangle = Distance between (-4, 0) and (2,0) = 2-(-4) = 6 units
Check the video explanation as mentioned below
