TS EAMCET 4-Aug-2021 Shift 1 Question Paper

Given, sides of triangles
x+y=6 . . . (i)
2x+y=4 . . . (ii)
x+2y=5‌‌... (iii)
From Eqs. (i) and (ii),
x=−2,y=8
From Eqs. (i) and (iii),
x=7,y=−1
From Eqs. (ii) and (iii),
x=1,y=2
Let vertices are A(−2,8),B(7,−1),C(1,2).
Let coordinate of circumcentre be P(h,k).
Then, PA=PB=PC
7)2+(k+1)2
⇒‌‌(h+2)2+(k−8)2‌‌=(h−7)2+(k+1)2
⇒‌‌h−k+1‌‌=0 . . . (iv)
PB‌‌=PC
‌PB2‌‌=PC2
⇒‌‌(h−7)2+(k+1)2‌‌=(h−1)2+(k−2)2
⇒‌‌‌−12h+6k+45‌‌=0 . . . (v)
From Eqs. (iv) and (v), we get
h=‌

17

2

,k=‌

19

2

∴ Circumcentre (‌

17

2

,‌

19

2

)