Questions & Answers - Ask Your Doubts

Ask your doubts to Learn New things everyday

Filters

All

Board/TargetAll

SubjectAll

GradeImportant Terms related to Triangles

TopicLatest Questions

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

(a) Centroid

(b) Incentre

(c) Circumcentre

(d) Orthocentre

What is the inradius of a right triangle with a height of $3$, base of $4$ and a hypotenuse of $5$?

$1)1$

$2)2$

$3)3$

$4)1.5$

$1)1$

$2)2$

$3)3$

$4)1.5$

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

(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

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 ?

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. $4$

A. $\dfrac{1}{2}$

B. $2$

C. $\dfrac{3}{2}$

D. $4$

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

\[1)\] The incentre.

\[2)\] The centroid.

\[3)\] The circumcentre

\[4)\] The orthocentre of the triangle

What is the relation between orthocenter, circumcentre, and centroid?

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) \[{{x}^{-2}}+{{y}^{-2}}+{{z}^{-2}}=9{{p}^{-2}}\]

(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) \[{{x}^{-2}}+{{y}^{-2}}+{{z}^{-2}}=9{{p}^{-2}}\]

If \[ABC\] is a triangle whose orthocenter is \[P\], circumcenter is \[Q\] then prove that \[\overline {QA} + \overline {QB} + \overline {QC} = \overline {QP} \]

Find the coordinates of the circumcentre of the triangle whose vertices are (8,6) , (8,2) and (2,2). Also find its circumradius.

The point of concurrency of three altitude of a triangle is called its

A.Incenter

B.Circumcenter

C.Centroid

D.Orthocenter

A.Incenter

B.Circumcenter

C.Centroid

D.Orthocenter

The right angled triangle circumcenter lies at the _______ of hypotenuse.

A.Inside

B.Outside

C.Midpoint

D.opposite

A.Inside

B.Outside

C.Midpoint

D.opposite

Prev

1

2

3

Next