Straight LineHardBloom L3
Question
The sides of a triangle are the straight lines $x + y = 1,7y = x$ and $\sqrt{3}y + x = 0$. Then which of the following is an interior point of the triangle:
Options
A.circumcenter
B.centroid
C.incentre
D.orthocenter
Solution
Sol. [Key Concept: The triangle from $x + y = 1,\ 7y = x,\ 3y + x = 0$ is obtuse, so only the centroid and incentre are interior.]
Triangle formed by lines is obtuse.
✘ (a) circumcentre lies outside an obtuse triangle.
✔ (b) centroid is always interior.
✔ (c) incentre is always interior.
✘ (d) orthocentre lies outside an obtuse triangle.
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