Question

The orthocenter, circumcenter, centroid and incenter of the triangle formed by the line $x+y=a$ with the coordinate axes lie on

• A. $x^2+y^2=1$
• B. $y=x$
• C. $y=2x$
• D. $y=3x$

Answer 1

Answer: (B)

$y=x$

The line $x+y=a$ cuts the coordinate axes at $A(a,0)$ and $B(0,a)$.

$\because$ circumcentre is the mid-point of $AB,$ i.e., $(\frac{a}{2},\frac{a}{2}),$

centroid is $(\frac{a}{3},\frac{a}{3}),$ orthocentre is the origin .

All lie on $y=x$.

Incentre lies on the angle bisector of $\angle AOB,$ Which is also $y=x.$