Trigonometry & Inverse Trigonometry
Circumcentre of Right Triangle from Lines
nta_pyq_2023_apr
Grade 11
Question:
Let $C(\alpha,\beta)$ be the circumcentre of the triangle formed by the lines $4x+3y=69$, $4y-3x=17$, and $x+7y=61$. Then $(\alpha-\beta)^2+\alpha+\beta$ is equal to
Step-by-Step Solution
Key Concept: Find vertices by solving pairs of lines. Check if one angle is $90°$; the circumcentre is the midpoint of the hypotenuse.
$C=(\frac{17}{2},\frac{15}{2})$. $(\alpha-\beta)^2+\alpha+\beta=1+16=17$.
Correct Answer: 2