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Question

The vertices of a triangle are A(1, 1), B(0, 0), and C(2, 0). The angular bisectors of the triangle meet at P. What are the coordinates of P?

This question was previously asked in
NDA 2 2025 GAT Question Paper (14-Sep-2025)
The correct answer is

(1, 1/2)

The coordinates of the point of intersection of the angle bisectors are (1, 1/2).

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Similar Questions

  1. The equation of the locus of a point equidistant from the points \((a, b)\) and \((c, d)\) is \((a-c)x + (b-d)y + k = 0\). What is the value of \(k\)?
  2. If a variable line passes through the point of intersection of the lines \(x + 2y - 1 = 0\) and \(2x - y - 1 = 0\) and meets the coordinate axes in \(A\) and \(B\), then what is the locus of the mid-point of \(AB\)?
  3. The number of points represented by the equation \(x = 5\) on the \(xy\)-plane is
  4. If p and q are real numbers between 0 and 1 such that the points (p, 1), (1, q), and (0, 0) form an equilateral triangle, then what is (p + q) equal to?

  5. Let A(3, -1) and B(1, 1) be the end points of line segment AB. Let P be the middle point of the line segment AB. Let Q be the point situated at a distance √2 units from P on the perpendicular bisector line of AB. What are the possible coordinates of Q?


Important Questions from Co-ordinate Geometry

  1. The graphs of the linear equations 4x - 2y = 10 and 4x + ky = 2 intersect at a point (a, 4). The value of k is equal to:

  2. In which ratio the point (-3, p) divides the line segment joining the points (-5, -4) and (-2, 3)?

  3. The area (in sq. units) of the triangle formed by the graphs of 8x + 3y = 24, 2x + 8 = y and the x-axis is:

  4. In which quadrant both abscissa and ordinate are negative?

  5. Find the slope of the line joining the points (3, -4) and (5, 2).

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