Test Details

Altitudes and Medians of a Triangle

Feb 11, 7:15 PM

90 minutes

Feb 11, 10:00 PM

46.0 marks

MCQ

24 questions

vinayak sir

Hi good morning students सर्व विद्यार्थी सकाळी आठ ते अकरा या वेळेत येथे उपस्थित राहतील काही अडचणी असल्यास आपण विचारू शकता सर्व विषयाचे तास सुरू आहेत

Class Details

Mathematics

Class 8th Scolership Exam

Mathematics

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Question Text

Question 1 :
ABC is a triangle and AD is median. If E is any point on AD, then

Question 2 :
The incenter, orthocenter, circumcenter, and centroid lie inside the triangle if it is

Question 3 :
If the orthocentre and centroid of a triangle are $(-3,5,1)$ and $(3,3,-1)$ respectively, then its circumcentre is

Question 4 :
If a vertex of a triangle is $(1 , 1)$ and the mid points of the two sides through this vertex are $(-1, 2)$ and $(3, 2)$, then the centroid of the triangle is

Question 5 :
If the middle points of the sides of a triangle be (-2, 3), (4, -3) and (4, 5) then centroid of triangle is

Question 7 :
In an equilateral triangle, centroid(G), circumcentre (C), orthocentre (H) and incentre (I)

Question 8 :
The point of concurrency of the medians of a triangle is known as_____.

Question 10 :
The vertices of a triangle are $(1,\sqrt {3}),(2\cos \theta,2\sin \theta)$ and $(2\sin \theta,-2\cos \theta)$ where $\theta\ \in \ R$. The locus of orthocentre of the triangle is

Question 11 :
In $\Delta ABC$, O is the orthocentre and $\angle BOC = 2 \angle A$, then the measure of $\angle BOC$ is equal to:

Question 12 :
Locus of the centroid of the triangle whose vertices are $(a \,cos \,t, a \,sin \,t), (b \,sin \,t, -b \,cos \,t)$ and $(1, 0)$, where $t$ is a parameter; is

Question 13 :
The centroid of the triangle formed by the lines $x+y=0 : 2x+y+5=0$ and $x-y=2$ is

Question 14 :
Let $A(-3, 2)$ and $B(-2, 1)$ be the vertices of a triangle ABC. If the centroid of triangle ABC lies on the line $3x+4y+2=0$ which doesn't pass through any vertex, then the locus of vertex C is?

Question 15 :
Let C be the centroid of the triangle with vertices $(3, -1)$, $(1, 3)$ and $(2, 4)$. Let P be the point of intersection of the lines $x+3y-1=0$ and $3x-y+1=0$. Then the line passing through the points C and P also passes through the point.

Question 16 :
If the distance from the vertex to the centroid of an equilateral triangle is $6$ cm, then what is the area of the triangle$?$

Question 17 :
Find the centroid of a triangle whose vertices are (2,3), (-4, 6) and (2, -6)

Question 18 :
Orthocentre of the triangle whose vertices are (0 , 0) , (3 , 4) and (0 , 4) is ,

Question 19 :
In $\Delta ABC$, if $A(1, -6), B(-5, 2)$ and the centroid is $G(-2, 1)$, then Co-ordinates of vertex $C$ are

Question 20 :
If D is any point on the side BC of $\Delta ABC$ such that $\Delta ADB$ and $\Delta ADC$ are equal in area, then

Question 21 :
If $p=a+b\omega+c\omega^2, q=b+c\omega+a\omega^2$, and $r=c+a\omega+b\omega^2$, where $a, b, c\neq 0$ and $\omega$ is the complex cube root of unity, then

Question 22 :
In $\triangle ABC$, if the orthocenter is $(1,2)$ and the circumceter is $(0,0)$, then centroid of $\triangle ABC$ is

Question 23 :
The point in the plane of a triangle which is at equal perpendicular distance from the sides of a triangle is its

Question 24 :
If $t_{1}+t_{2}+t_{3}=-t_{1}t_{2}t_{3}$, then the orthocentre of the triangle formed by the points $\left ( at_{1}t_{2}, a\left ( t_{1}+t_{2} \right ) \right )$, $\left ( at_{2}t_3, a\left ( t_{2}+t_{3} \right ) \right )$ and $\left ( at_{3}t_{1}, a\left ( t_{3}+t_{1} \right ) \right )$ lies on:

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