Question 203333: Points X, Y and Z lie on the sides of triangle ABC so that segments AX, BY and CZ, if drawn, would intersect at one interior point P. Using 3 of these 7 points at a time as vertices, how many triangles can be formed?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! ): Points X, Y and Z lie on the sides of triangle ABC so that segments AX, BY and CZ, if drawn, would intersect at one interior point P. Using 3 of these 7 points at a time as vertices, how many triangles can be formed?
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Draw the picture.
Three points determine a triangle unless the three are collinear.
There are 7C3= 25 sets of three points.
6 of those sets are collinear.
Therefore 29 triangles can be formed.
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Cheers,
Stan H.
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