Straight Lines
Incentre of Triangle from Midpoints
nta_pyq_2023_apr
Grade 11
Question:
Let $A(0,1)$, $B(1,1)$ and $C(1,0)$ be the midpoints of sides of a triangle with incentre $D$. If the focus of $y^2=4ax$ through $D$ is $(\alpha+\beta\sqrt{2},0)$, then $\dfrac{\alpha}{\beta^2}$ is equal to
Step-by-Step Solution
Key Concept: Find the triangle from midpoints, then compute incentre. Use the focus of the parabola.
$\frac{\alpha}{\beta^2}=8$.
Correct Answer: 1