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Find the coordinates of the circumcenter of triangle whose vertices are A (5, -1), B (-1, 5) and C (6, 6).

Option: 1

\left ( \frac{21}{8} ,\frac{21}{8}\right )
 


Option: 2

\left ( \frac{23}{8} ,\frac{23}{8}\right )


Option: 3

\left ( \frac{21}{8} ,\frac{23}{8}\right )

 


Option: 4

\left ( \frac{23}{8} ,\frac{21}{8}\right )


Answers (1)

best_answer

As we learnt

Circumcircle: A circle circumscribing a triangle.

 

Let P (x, y) be the circumcentre of the triangle ABC

So, PA = PB = PC (As all of these equal the radius of the circumcircle)

 ⇒ PA2 = PB2 = PC2

Using PA2 = PB2 

⇒ (x - 5)2 + (y + 1)2 = (x + 1)2 + (y - 5)2

⇒ x2- 10x + 25 + y2 + 2y + 1 = x2 + 2x + 1 + y2- 10y + 25

⇒ x - y = 0                        … (1)

Now using PB2 = PC2                         

(x + 1)2 + (y - 5)2 = (x - 6)2 + (y - 6)2

⇒  7x + y - 23 = 0.            … (2)

From (1) and (2), we get

x= \frac{23}{8}= y

Hence the coordinates of the circumcentre are \left ( \frac{23}{8} ,\frac{23}{8}\right )

Posted by

shivangi.bhatnagar

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