If the line x-y-1-0 passes through the circumcentre and the point B of a triangle A B C- where - B-90- Then the other two vertices apart from B of the triangle can lie on the lineA- x-y-1-0B- 2 x - y -1-0C- x-2 y-1-0D- x-y-1-0

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If the line x...

Question

If the line x+y-1 = 0 passes through the circumcentre and the point B of a triangle ABC, where $∠$ B = $90^{\circ}$ . Then the other two vertices (apart from B) of the triangle can lie on the line

x + y + 1 =0

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2x + y + 1 =0

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x –y +1= 0

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x + 2y - 1 =0

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Solution

The correct option is C
x –y +1= 0

Given that the triangle is a right angled triangle. The circumcentre of the triangle is the midpoint of the hypotenuse. So given that the line x+y-1 = 0 passes through the circumcentre, so the other two vertices apart from B lie on a line perpendicular to given line with slope 1.

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If the line x+y-1 = 0 passes through the circumcentre and the point B of a triangle ABC, where ∠B = 90∘. Then the other two vertices (apart from B) of the triangle can lie on the line

If the line x+y-1 = 0 passes through the circumcentre and the point B of a triangle ABC, where $∠$ B = $90^{\circ}$ . Then the other two vertices (apart from B) of the triangle can lie on the line