Cool geometry problem-3

Geometry Level 3

Let $\text O$ be a point inside $\triangle ABC$ . Three straight lines are pass through $\text O$ parallelly to the sides of the triangle. The lines divide the triangle into six parts, three of which are triangles of areas $S_{1}, S_{2}$ and $S_{3}$ . If $S$ is the area of $\triangle ABC$ .

Which of the following is true ?

S = \sqrt{ S_{1}S_{2}S_{3} }

S = ( \sqrt{S_{1}} + \sqrt{S_{2}} + \sqrt{S_{3}} )^{2}

S = \sqrt{ S_{1}S_{2} } + \sqrt{ S_{2}S_{3} }+ \sqrt{ S_{3}S_{1} }

S =( S_{1} + S_{2} + S_{3} )^{2}

1 solution

Rahul Paswan
Jan 17, 2015

Nice solution Banti.Haven't seen questions & solutions from you for long time now.Earlier you posted some very intriguing geometry questions. Hope the same we see again from your side on brilliant.

Deepak Kumar - 4 years, 12 months ago

Cool geometry problem-3

1 solution

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