Question

Which of the following statements is/are true?

(1) In an isosceles triangle, the incentre, the circumcentre, the centroid and the orthocentre lie in a straight line.

(2) In an equilateral triangle, the incentre, the centroid and the circumcentre are one and the same point.

(3) The centroid and the orthocenter of a triangle always lie inside a triangle.

(4) Only in an acute angled triangle, the incentre lies inside the triangle.

Answer 1

lol lets see them one but one hehe

Answer 2

by*

Answer 3

we can eliminate option (3) i guess
http://www.mathopenref.com/triangleorthocenter.html

Answer 4

need to work rest of the options

Answer 5

okkkk ill see 1 :P

Answer 6

4th one is also not the option

Answer 7

mmmm

Answer 8

ok its always 2 lol

Answer 9

(1) is true ?

yes we can eliminate (3) and (4) safely

Answer 10

1 is not always true

Answer 11

The orthocenter, the centroid and the circumcenter of a non-equilateral triangle are aligned; that is to say, they belong to the same straight line, called line of Euler.

Answer 12

mmm then it should be true for isosceles triangle ?
nice !

Answer 13

so it is isosceles

Answer 14

Euler again xD

Answer 15

ok so we need to check if incentre on the same line as well

Answer 16

yes

Answer 17

yes it also incentre option 1 is correct

Answer 18

In an acute triangle, the 4 centers are all inside the triangle:

Answer 19

how did u got incentre on the same line ?

Answer 20

so 4 is also correct

Answer 21

4 is wrong lol

Answer 22

In an isosceles triangle, the 4 centers are collinear. This is true because in an isosceles triangle, the altitude to the base is also a median and an angle bisector. This line is the one line of reflection symmetry for the triangle

Answer 23

nice !

Answer 24

not colinear ?

Answer 25

its lie inside the triangle

Answer 26

?

Answer 27

acute angle .see the th option they asked for whether its lie inside the acute triangle

Answer 28

(4) Only in an acute angled triangle, the incentre lies inside the triangle.

its wrong since it says "Only"
, the incentre lies inside the triangle all the time no matter what angle was

Answer 29

yes u are right!i didnt see only

Answer 30

^^

Answer 31

2 is also the right option

Answer 32

In an equilateral triangle, all centers are the same point. This is because the altitude to each side of an equilateral triangle is also a median and an angle bisector. The equilateral triangle is the most symmetrical triangle of all, and has 3 lines of reflection symmetry (those same altitudes). The equilateral triangle has 120 degree rotation symmetry about the "center" (Orthocenter, Centroid, Circumcenter, and Incenter). The equilateral triangle is the only triangle that does have rotation symmetry.

Answer 33

so 1 and 2

Answer 34

well lol as u say ,
but me dint convince yet
mmm ill check it by my own ^_^

Answer 35

k .i will show you the image

Answer 36

not sure about 2
but 1 is correct

Answer 37

well what if it was obtuse triangle ?
mmm

Answer 38

In an obtuse triangle, the Circumcenter and Orthocenter are outside the triangle, while the other 2 centers are inside the triangle.

Answer 39

this is equvilant im not sure about 2 not 1

Answer 40

wait im not sure about 1
2 is correct *sigh*
can't focus with u lol