NTSE Stage 2 SAT 2019 Exam Question Paper

Question : 58 of 100

Marks: +1, -0

A circle passes through the vertices of a triangle ABC. If the vertices are

A(-2,5),B(-2,-3),C(2,-3)

, then the centre of the circle is

Solution:

Let 0 (jc, y) is the centre of the given circle.
Join OA, OB & OC.
∵ OA = OB = OC

∴OA^{2}=OB^{2}

⇒√{(x+2)^{2}+(y-5)^{2}}=√{(x+2)^{2}+(y+3)^{2}}

⇒x^{2}+4+4x+y^{2}+25-10y=x^{2}+4+4x+y^{2}+9+6x

⇒16y=16⇒y=1

Again

OB^2=OC^2

⇒√{(x+2)^{2}+(y+3)^{2}}=√{(x-2)^{2}+(y+3)^{2}}

⇒x^{2}+4+4x+(y+3)^{2}=x^{2}+4-4x+(y+3)^{2}

⇒8x=0⇒x=0

∴ centre of the circle is (0, 1)

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