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Question

Find the coordinates of the circumcentre of the triangle whose vertices are (8, 6), (8, – 2) and (2, – 2). Also, find its circumradius. [3 MARKS]

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Solution

Concept : 1 Mark
Application : 1 Mark
Calculation : 1 Mark

Recall that the circumcentre of a traingle is equidistatnt from the verices of a traingle.

Let A (8 , 6 ), B ( 8, -2 ) and C (2 , -2) be the vertices of the given traingle.

and let P ( x, y) be the circumcentre of this traingle . Then,

PA=PB=PCPA2=PB2=PC2

Now ,

PA2=PB2

(x8)2+(y6)2=(x8)2+(y+2)2

x2+y216x12y+100=x2+y216x+4y+68

16y=32

y=2

and

PB2=PC2

(x8)2+(y+2)2=(x2)2+(y+2)2

x2+y216x+4y+68=x2+y24x+4y+8

12x=60

x=5

So the coordinates of the circumcentre P are (5 ,2)

Also, Circum- radius = PA = PB = PC

=((58)2+(26)2)

=9+16

=5


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