Question

uestion(4)
The vertices of a triangle are (6,0),(0,6), and (6,6). Then the distance between its circumcentre and orthocenter is


$6 \sqrt{2}$
​

Answer 1

Final Answer : √2 units

Steps:

1) Let there be triangle ABC, where

A = (6,0)

B = (0,6)

C = (6,6)

Clearly,

We observe that ABC is right -angled triangle.

2) In right - angled triangle, circumcentre is mid-point of hypotenuse.

Here, BA is hypotenuse .

So, Mid point of AB

D = ((0+6)/2 ,(6+0)/2 )

= (3,3)

Hence, Circumcentre is D(3,3).

3) And, Centroid

E = (6+0+6)/3 , (0+6+6)/3

E = (4,4)

Therefore, Distance between Centroid and Circumvented is ED

Hence, Distance between Circumcentre and Centroid of triangle is

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Answer 2

Answer:

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