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If {({b}_{{2}}-{b}_{{1}})}{({b}_{{3}}-{b}_{{1}})}+{({a}_{{2}}-

Question

If $(b_{2} - b_{1}) (b_{3} - b_{1}) + (a_{2} - a_{1}) (a_{3} - a_{1}) = 0$ , then prove that the circumcenter of the triangle having vertices $(a_{1}, b_{1}), (a_{2}, b_{2})$ and $(a_{3}, b_{3})$ is $(\frac{a _{2 + a_{3}}}{2}, \frac{b _{2 +} b _{3}}{2})$

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(b_{2} - b_{1}) (b_{3} - b_{1}) + (a_{2} - a_{1}) (a_{3} - a_{1}) = 0

, then prove that the circumcenter of the triangle having vertices

(a_{1}, b_{1}), (a_{2}, b_{2})

and

(a_{3}, b_{3})

(\frac{a _{2 + a_{3}}}{2}, \frac{b _{2 +} b _{3}}{2})

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Question Text

(b_{2} - b_{1}) (b_{3} - b_{1}) + (a_{2} - a_{1}) (a_{3} - a_{1}) = 0

, then prove that the circumcenter of the triangle having vertices

(a_{1}, b_{1}), (a_{2}, b_{2})

and

(a_{3}, b_{3})

(\frac{a _{2 + a_{3}}}{2}, \frac{b _{2 +} b _{3}}{2})

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