88292 The centroid of the triangle formed by the lines \(x+y=1,2 x+3 y=6\) and \(4 x-y=-4\) lies in the quadrant

88298 The distance of the origin from the centroid of the triangle whose two sides have the equations \(x-2 y+1=0\) and \(2 x-y-1=0\) and whose orthocenter is \(\left(\frac{7}{3}, \frac{7}{3}\right)\) is :

88293 Let the circumcentre of a triangle with vertices \(A(a, 3), B(b, 5)\) and \(C(a, b), a b>0\) be \(P(1,1)\). If the line AP intersects the line \(B C\) at the point \(Q\left(k_{1}, k_{2}\right)\), then \(k_{1}+k_{2}\) is equal to:

88294 Let \(A(1,1), B(-4,3), C(-2,-5)\) be vertices of a triangle \(A B C, P\) be a point on side \(B C\), and \(\Delta_{1}\) and \(\Delta_{2}\) be the areas of triangles \(A P B\) and \(A B C\), respectively. If \(\Delta_{1}: \Delta_{2}: 4: 7\), then the area enclosed by the lines \(A P, A C\) and the \(x\)-axis is

88295 Consider two points \(A(a, b)\) and \(B(c, d)\) where \(c>a>0\) and \(d>b>0\), then abscissa of a point on \(x\)-axis such that sum of its distances from \(A\) and \(B\) is minimum, is :

88292 The centroid of the triangle formed by the lines \(x+y=1,2 x+3 y=6\) and \(4 x-y=-4\) lies in the quadrant

88298 The distance of the origin from the centroid of the triangle whose two sides have the equations \(x-2 y+1=0\) and \(2 x-y-1=0\) and whose orthocenter is \(\left(\frac{7}{3}, \frac{7}{3}\right)\) is :

88293 Let the circumcentre of a triangle with vertices \(A(a, 3), B(b, 5)\) and \(C(a, b), a b>0\) be \(P(1,1)\). If the line AP intersects the line \(B C\) at the point \(Q\left(k_{1}, k_{2}\right)\), then \(k_{1}+k_{2}\) is equal to:

88294 Let \(A(1,1), B(-4,3), C(-2,-5)\) be vertices of a triangle \(A B C, P\) be a point on side \(B C\), and \(\Delta_{1}\) and \(\Delta_{2}\) be the areas of triangles \(A P B\) and \(A B C\), respectively. If \(\Delta_{1}: \Delta_{2}: 4: 7\), then the area enclosed by the lines \(A P, A C\) and the \(x\)-axis is

88295 Consider two points \(A(a, b)\) and \(B(c, d)\) where \(c>a>0\) and \(d>b>0\), then abscissa of a point on \(x\)-axis such that sum of its distances from \(A\) and \(B\) is minimum, is :

88292 The centroid of the triangle formed by the lines \(x+y=1,2 x+3 y=6\) and \(4 x-y=-4\) lies in the quadrant

88298 The distance of the origin from the centroid of the triangle whose two sides have the equations \(x-2 y+1=0\) and \(2 x-y-1=0\) and whose orthocenter is \(\left(\frac{7}{3}, \frac{7}{3}\right)\) is :

88293 Let the circumcentre of a triangle with vertices \(A(a, 3), B(b, 5)\) and \(C(a, b), a b>0\) be \(P(1,1)\). If the line AP intersects the line \(B C\) at the point \(Q\left(k_{1}, k_{2}\right)\), then \(k_{1}+k_{2}\) is equal to:

88294 Let \(A(1,1), B(-4,3), C(-2,-5)\) be vertices of a triangle \(A B C, P\) be a point on side \(B C\), and \(\Delta_{1}\) and \(\Delta_{2}\) be the areas of triangles \(A P B\) and \(A B C\), respectively. If \(\Delta_{1}: \Delta_{2}: 4: 7\), then the area enclosed by the lines \(A P, A C\) and the \(x\)-axis is

88295 Consider two points \(A(a, b)\) and \(B(c, d)\) where \(c>a>0\) and \(d>b>0\), then abscissa of a point on \(x\)-axis such that sum of its distances from \(A\) and \(B\) is minimum, is :

88292 The centroid of the triangle formed by the lines \(x+y=1,2 x+3 y=6\) and \(4 x-y=-4\) lies in the quadrant

88298 The distance of the origin from the centroid of the triangle whose two sides have the equations \(x-2 y+1=0\) and \(2 x-y-1=0\) and whose orthocenter is \(\left(\frac{7}{3}, \frac{7}{3}\right)\) is :

88293 Let the circumcentre of a triangle with vertices \(A(a, 3), B(b, 5)\) and \(C(a, b), a b>0\) be \(P(1,1)\). If the line AP intersects the line \(B C\) at the point \(Q\left(k_{1}, k_{2}\right)\), then \(k_{1}+k_{2}\) is equal to:

88294 Let \(A(1,1), B(-4,3), C(-2,-5)\) be vertices of a triangle \(A B C, P\) be a point on side \(B C\), and \(\Delta_{1}\) and \(\Delta_{2}\) be the areas of triangles \(A P B\) and \(A B C\), respectively. If \(\Delta_{1}: \Delta_{2}: 4: 7\), then the area enclosed by the lines \(A P, A C\) and the \(x\)-axis is

88295 Consider two points \(A(a, b)\) and \(B(c, d)\) where \(c>a>0\) and \(d>b>0\), then abscissa of a point on \(x\)-axis such that sum of its distances from \(A\) and \(B\) is minimum, is :

88292 The centroid of the triangle formed by the lines \(x+y=1,2 x+3 y=6\) and \(4 x-y=-4\) lies in the quadrant

88298 The distance of the origin from the centroid of the triangle whose two sides have the equations \(x-2 y+1=0\) and \(2 x-y-1=0\) and whose orthocenter is \(\left(\frac{7}{3}, \frac{7}{3}\right)\) is :

88293 Let the circumcentre of a triangle with vertices \(A(a, 3), B(b, 5)\) and \(C(a, b), a b>0\) be \(P(1,1)\). If the line AP intersects the line \(B C\) at the point \(Q\left(k_{1}, k_{2}\right)\), then \(k_{1}+k_{2}\) is equal to:

88294 Let \(A(1,1), B(-4,3), C(-2,-5)\) be vertices of a triangle \(A B C, P\) be a point on side \(B C\), and \(\Delta_{1}\) and \(\Delta_{2}\) be the areas of triangles \(A P B\) and \(A B C\), respectively. If \(\Delta_{1}: \Delta_{2}: 4: 7\), then the area enclosed by the lines \(A P, A C\) and the \(x\)-axis is

88295 Consider two points \(A(a, b)\) and \(B(c, d)\) where \(c>a>0\) and \(d>b>0\), then abscissa of a point on \(x\)-axis such that sum of its distances from \(A\) and \(B\) is minimum, is :