For the triangle whose sides are $x + y - 6 = 0, 7 x + y - 6 = 0 and x - 7 y = 6$ , the co-ordinates of the incentre are:

$(\frac{12}{5}, \frac{6}{5})$

$(\frac{3}{4}, - \frac{1}{7})$

$(- 1, 5)$

None of these

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The correct Answer is:A

Updated on:21/07/2023

Question 1 - Select One
Incentre of the triangle whose vertices are (6, 0), (0, 6) and (7, 7), is
A $(\frac{9}{2}, \frac{9}{2})$
B $(\frac{7}{2}, \frac{7}{2})$
C $(\frac{11}{2}, \frac{11}{2})$
Dnone of these
Question 1 - Select One
Three sides of a triangle are represented by the equation $x + y - 6 = 0, 2 x + y - 4 = 0 and x + 2 y - 5 = 0 .$ The co-ordinate of its orthocentre of
A $(10, 11)$
B $(2, 3)$
C $(- 2, - 3)$
D $(- 11, - 10)$
Question 1 - Select One
Orthocentre of the triangle whose sides are given by 4x - 7y + 10= 0, x + y - 5 = 0 & 7x + 4y - 15 = 0 is
A( -1, -2)
B(1, -2)
C(-1, 2)
D(1, 2)
Question 1 - Select One
The equation x+2y=3,y-2x=1 and 7x-6y+a=0 are consisten for
Aa=7
Ba=1
Ca=11
DNone of these
Question 1 - Select One
The radical centre of three circles described on the three sides
$4 x - 7 y + 10 = 0, x + y - 5 = 0 and 7 x + 4 y - 15 = 0$ of a triangle as diameters is
A $(2, 1)$
B $(1, 2)$
C $(2, 3)$
D $(- 6, - 2)$