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Mathematics
Important terms related to triangles
If the vertices P,Q,R of a triangle PQR are rational points, which of the following points of the triangle PQR is (are) always rational point(s) ?
(a) Centroid
(b) Incentre
(c) Circumcentre
(d) Orthocentre
Mathematics
Important terms related to triangles
What is the inradius of a right triangle with a height of $3$, base of $4$ and a hypotenuse of $5$?
$1)1$
$2)2$
$3)3$
$4)1.5$

Mathematics
Important terms related to triangles
Find the solution for the bisector AG of triangle ABC in terms of vectors ‘a’ and ‘b’. Given that: G is the centroid of the triangle ABC if \[{\text{AB = a}}\],${\text{AC = b}}$ respectively.
(a) ${\text{AG = }}\dfrac{{\bar a - \bar b}}{3}$
(b) ${\text{AG = }}\dfrac{{\bar a + \bar b}}{3}$
(c) ${\text{AG = }}\dfrac{{\bar a + \bar b}}{2}$
(d) None of the above

Mathematics
Important terms related to triangles
Let the orthocentre and centroid of the triangle \[A( - 3,5)\] and \[B(3,3)\] respectively. IF $C$ is the circumcenter of the triangle, then the radius of the circle having the segment $AC$ as diameter is ?
Mathematics
Important terms related to triangles
A triangle is inscribed in a circle of radius $1$. The distance between the orthocentre and the circumcentre of the triangle cannot be
A. $\dfrac{1}{2}$
B. $2$
C. $\dfrac{3}{2}$
D. $4$
Mathematics
Important terms related to triangles
The equations to the sides of a triangle are \[x-3y=0\] , \[4x+3y=0\] and \[3x+y=0\] . Then line \[3x-4y=0\] passes through
 \[1)\] The incentre.
 \[2)\] The centroid.
 \[3)\] The circumcentre
 \[4)\] The orthocentre of the triangle
Mathematics
Important terms related to triangles
What is the relation between orthocenter, circumcentre, and centroid?
Mathematics
Important terms related to triangles
A variable plane is at a constant distance p from the origin and meets the axes in A, B and C. The locus of the centroid of the triangle ABC is
(a) \[{{x}^{-2}}+{{y}^{-2}}+{{z}^{-2}}={{p}^{-2}}\]
(b) \[{{x}^{-2}}+{{y}^{-2}}+{{z}^{-2}}=4{{p}^{-2}}\]
(c) \[{{x}^{-2}}+{{y}^{-2}}+{{z}^{-2}}=16{{p}^{-2}}\]
(d) \[{{x}^{-2}}+{{y}^{-2}}+{{z}^{-2}}=9{{p}^{-2}}\]
Mathematics
Important terms related to triangles
If \[ABC\] is a triangle whose orthocenter is \[P\], circumcenter is \[Q\] then prove that \[\overline {QA} + \overline {QB} + \overline {QC} = \overline {QP} \]
Mathematics
Important terms related to triangles
Find the coordinates of the circumcentre of the triangle whose vertices are (8,6) , (8,2) and (2,2). Also find its circumradius.
Mathematics
Important terms related to triangles
The point of concurrency of three altitude of a triangle is called its
A.Incenter
B.Circumcenter
C.Centroid
D.Orthocenter

Mathematics
Important terms related to triangles
The right angled triangle circumcenter lies at the _______ of hypotenuse.
A.Inside
B.Outside
C.Midpoint
D.opposite
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