Question

it's option is c

I want solutions ​

Answer 1

Answer:

Hope this is OK for you completely

Answer 2

$\sf{Answer}$

Given :-

• Centroid of a triangle is (1 ,2 )
• Orthocentre of a triangle is (9,-2)

To find :-

• Circumcentre of a triangle

Concept to know :-

The centroid divides Orthocentre and circumcentre internally in ratio 2 : 1 By using this concept we can solve And here For finding Co-ordinates of Circumcentre we also have to use section formula using ratio m:n = 2:1

Section formula:-

$\sf\dfrac{mx_2 +nx_1}{m+n}$, $\sf\dfrac{my_2 +ny_1}{m+n}$

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Lets Solve Now !

So,

Let the cordinates of Circumcentre be (x,y)

Cordinates of Orthocentre = (9,-6)

Now,

$\sf{x_1 = 9}$

$\sf{x_2 = x}$

$\sf{y_1 = -6}$

$\sf{y_2=y}$

m : n = 2:1

Now,

$\sf\dfrac{mx_2 +nx_1}{m+n}$, $\sf\dfrac{my_2 +ny_1}{m+n}$ = G

(1 ,2 ) = $\sf\dfrac{2(x) + (1)9}{2+1}$, $\sf\dfrac{2(y) +(1)-6}{1+2}$

(1,2) = $\sf\dfrac{2x+9}{3}$, $\sf\dfrac{2y-6}{3}$

Now, both equating to x axis , y axis

$\sf\dfrac{2x+9}{3}$ = 1

Do cross multiplication

2x + 9 = 3

2x = 3-9

2x = -6

x = -3

$\sf\dfrac{2y-6}{3}$ = 2

Do cross multiplication

2y - 6 = 6

2y = 6+6

2y = 12

y = 6

So (x,y) = (-3,6)

So, cordinates of Circumcentre is (-3,6)

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Know more:-

Centroid :- The point of intersection of three medians in a triangle is called Centroid

Incentre :- The point of conccurence of internal angular bisectors is called Incentre

Excentre :- The point of concurrence of 1 internal angular bisector 2 External angular bisectors is called excentre

Circumcentre :- The point of intersection of perpendicular bisectors of triangle is called circumcentre

Orthocentre :- The altitude of triangle are concurrent and their point of concurrence is called Orthocentre

These are the some important terms that You have to remember