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In triangle ABC, A=(1,2) B=(5,5), ∠ACB=90°.

If area of △ABC is to be 6.5 square units, then the possible number of points for C is

Let the coordinate of point C be (x,y)

AB = \(\sqrt{(1-5)^2 + (2-5)^2} = \sqrt{4^2 + 3^2} = 5\)

Let us find a point C(x,y) on the circumference of a circle with diameter AB such that area of triangle formed △ABC is to be 6.5 square units.

Radius of the circle = 5/2 = 2.5 units

Area of triangle △ABC = 1/2* base * height = 1/2*AB*h = 1/2 *5 *h = 6.5
h = 6.5/2.5 = 2.6 units

But hmax = 2.5 since h can not exceed radius of the circle

Not such triangle is possible

IMO A
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