Question

Circum centre of the triangle formed by the points (3, 2), (3, -2), (5,2) is

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Answer 1

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Answer 2

Concept

The intersection or meeting of three perpendicular bisectors from a triangle's sides is known as the circumcenter. The point of concurrency of a triangle is another name for a triangle's circumcenter.

Given

The coordinates of vertices of triangle are $(3, 2), (3, -2), (5,2)$.

To Find

We have to find the coordinate of circumcenter of the triangle.

Solution

According to the problem,

Let the coordinate of the circumcenter be (h,k)

In case of A and B,

$(h-3)^{2} +(k-2)^2=(h-5)^2+(k-2)^2$

⇒$h^2-6h+9+k^2-4k+4=h^2-10h+25+k^2-4k+4$

⇒$-6h+10h=29-13$

⇒$h=4$

In case of A and C,

$(h-3)^{2} +(k-2)^2=(h-3)^2+(k+2)^2$

⇒$(k-2)^2=(k+2)^2$

⇒$-4k=4k$

⇒$8k=0$

⇒$k=0$

Hence, circumcenter (h,k) is $(4,0)$.

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