The vertices of a triangle are (0, 0), (4, 0) and (3, 9). The area of the circle passing through these three points is
Explanation:
The diagram can be drawn as follows:
Height of the given triangle = 9 and base = 4
∴ Area of the triangle = 12×9×4 = 18
We know area of a triangle = abc/4R
(where a, b, and c are the sides of the triangle and R is the circumradius)
a = AB = 4 units b = BC = 92+12=82 units c = AC = 32+92=90 units
The sides of the triangle are 4, √82 and √90
⇒ 18 = 4×82×904R
⇒ R = 2053
∴ Area of the circumcircle = πR2 = 205π9
Hence, option (b).
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