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Question

In given figure let A(0,0) and B(8,0) be two vertices of a right angled triangle whose hypotenuse is BC. If the circumcentre is (4,2), then the point C is
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A
(2,4)
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B
(0,8)
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C
(0,4)
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D
(0,6)
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E
(2,8)
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Solution

The correct option is B (0,4)
In a right angle triangle, the mid-point of the hypotenuse is the circumcentre.
Let the coordinates of the point C be (x,y).

Then,by using Midpoint formula X=(x1+x22)andY=(y1+y22)

(8+x2,0+y2)=(4,2)

8+x2=4 and 0+y2=2

x=0 and y=4

Hence, coordinates of C are (0,4).

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