Lines p, q and r are concurrent. Also lines p, s and t are concurrent. Is it always true that the lines q, r and s will be concurrent? Is it always true for lines q, r and t?

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Solution

Lines p, q, and r are concurrent. So, lines p, q and r intersect at a common point O.

Given lines p, s and t are concurrent. So, lines p, s and t also intersect at a common point.
However, it is not always true that q, r and s or q, r and t are concurrent.

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Lines p, q and r are concurrent. Also lines p, s and t are concurrent. Is it always true that the lines q, r and s will be concurrent? Is it always true for lines q, r and t?

Lines p, q, and r are concurrent. So, lines p, q and r intersect at a common point O. Given lines p, s and t are concurrent. So, lines p, s and t also intersect at a common point. However, it is not always true that q, r and s or q, r and t are concurrent.

Lines p, q, and r are concurrent. So, lines p, q and r intersect at a common point O.

Given lines p, s and t are concurrent. So, lines p, s and t also intersect at a common point.
However, it is not always true that q, r and s or q, r and t are concurrent.