Question

Orthocentre of the triangle is (2,1) and the circumcentre is (7/2,5/2) then its nine point circle cebtre is

Answer 1

Step-by-step explanation:

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Let..

Orthocentre = (2,1) = (x1, y1)

Circumcentre = (7/2 , 5/2) = (x2,y2)

Something important to note before using my method....

[

You can remember the ratio,

ONGC

(Oil Natural Gas Corporation)

Where,

O is Orthocentre

N is Nine point circle centre

G is Centroid

C is Circumcentre

]

So Nine point circle centre divides Orthocentre and Circumcentre in 1: 2

m:n = 1:2

m = 1

n = 2

So,

By using section formula..

$x = \frac{mx2 + nx1}{m + n} \: \: \: \: y = \frac{my2 + ny1}{m + n} \\ x = \frac{ \frac{7}{2} + 2(2) }{3} \: \: \: \: \: \: \: \: \: y = \frac{ \frac{5}{2} + 2(1)}{3} \\ x = \frac{15}{6} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: y = \frac{9}{6} \\ x = \frac{5}{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: y = \frac{3}{2} \\ \\ (x</em><em>,</em><em>y) = ( \frac{5}{2} </em><em>,</em><em> </em><em>\frac{3}{2} )$

So,

Nine point circle centre is (5/2 , 3/2)

Thank the answer if it helps so....