JEE Main 2026 Apr 4 Shift 1, Mathematics Q12: Introduction to Circles

JEE Main2026Apr 4, Shift 1Mathematics

Let the vertex $A$ of a triangle $A B C$ be $(1, 2)$ , and the mid-point of the side $A B$ be $(5, - 1)$ . If the centroid of this triangle is $(3, 4)$ and its circumcenter is $(α, β)$ , then $21 (α + β)$ is equal to:

A
$309$
B
$403$
C
$497$
D
$524$

Solution

equation of PM : $4 x - 3 y = 23$

equation of PM : $5 x - 9 y = - 25$

$P (\frac{94}{7}, \frac{215}{21})$

$21 (α + β) = 497$

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JEE Main 2026 Apr 4 Shift 1, Mathematics Q12: Introduction to Circles

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