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MathsMediumMCQ2022 · 29 Jul Shift 1

Q63.Let the circumcentre of a triangle with vertices A(a, 3), B(b, 5) and C(a, b), ab > 0 be P(1, 1). If the line AP intersects the line BC at the point Q(k1, k2), then k1 + k2 is equal to (1) 2 (2) 47 (3) 2 (4) 4 7

What This Question Tests

This question tests the understanding of the circumcenter's property (equidistance from vertices) to find coordinates, followed by forming equations of lines and finding their intersection.

Concepts Tested

Circumcenter propertiesEquation of a lineIntersection of lines

Formulas Used

Distance formula: d² = (x₂-x₁)² + (y₂-y₁)²

Slope of a line: m = (y₂-y₁)/(x₂-x₁)

Equation of a line: y - y₁ = m(x - x₁)

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