JEE Main 2026 · 4 Apr · Shift 1 · Mathematics Q12

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MathematicsSingle correct+4 / -1Question 12 of 75

Let the vertex A of a triangle ABC be $(1,2)$ , and the mid-point of the side AB be $(5,-1)$ . If the centroid of this triangle is $(3,4)$ and its circumcenter is $(\alpha,\beta)$ , then $21(\alpha+\beta)$ is equal to:

309

403

497

524

Answer and worked solution

Official answer: C

Vertices. $B=2(5,-1)-(1,2)=(9,-4)$ and $C=3(3,4)-A-B=(-1,14)$ .

Perpendicular bisectors.

AB: through $(5,-1)$ , normal $(8,-6)$ : $4x-3y=23$ .
AC: through $(0,8)$ , normal $(-2,12)$ : $-x+6y=48$ .

Solve. $y=\frac{215}{21}$ , $x=\frac{282}{21}$ , so $21(\alpha+\beta)=497$ .

(C)

Topics:Distance and section formulae Equations of a line

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JEE Main 2026 · 4 Apr · Shift 1, Mathematics question 12