Three congruent circles have a common point 0 and lie inside a given triangle. Each circle touches a pair of sides of the triangle. Prove that the in-centre and the circum-centre of the triangle and the common point 0 are collinear.
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Problem 1
$\displaystyle P$ is a point inside a given triangle $\displaystyle ABC$. $\displaystyle D, E, F$ are the feet of the perpendiculars from $\displaystyle P$ to the lines $\displaystyle BC, CA, AB$, respectively. Find all $\displaystyle P$ for which
$\frac{BC}{PD} + \frac{CA}{PE} + \frac{AB}{PF}$
is least.
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$\displaystyle P$ is a point inside a given triangle $\displaystyle ABC$. $\displaystyle D, E, F$ are the feet of the perpendiculars from $\displaystyle P$ to the lines $\displaystyle BC, CA, AB$, respectively. Find all $\displaystyle P$ for which
$\frac{BC}{PD} + \frac{CA}{PE} + \frac{AB}{PF}$
is least.
Mark me Brainly:)
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