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If P is the center of the circle shown above, and BAC=30º, and the area of triangle ABC is 6, what is the area of the circle?
A. (√3)π
B. (2√3)π
C. 4π
D. 6π
E. (4√3)π
Attachment:
1.png [ 7.35 KiB | Viewed 1547 times ]
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28 Jun 2022, 21:27
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If P is the center of the circle shown above, and BAC=30º, and the area of triangle ABC is 6, what is the area of the circle?
A. (√3)π
B. (2√3)π
C. 4π
D. 6π
E. (4√3)π
Attachment:
1.png
Since this is a 30:60:90 triangle we have the sides in the ratio 1:√3:2
Lets say we have the sides as a, √3a and 2a
Now 1/2 * a * √3a = 6
=> a^2 = 4√3
Now a is the radius of the circle basis the dimension ratios of the triangle
Hence area of circle = a^2 * π = (4√3)π
Option E
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