Triangles in Intersecting Families

We prove the following the generalized Turan type result. A collection tau of r sets is an r-triangle if for every T1, T2,.,T-1 is an element of tau we have boolean AND(r=1)(l-1) not equal theta, but boolean AND(T is an element of tau) T is empty. A family F of sets is r-wise intersecting if for any F-1, F-2,....,F-r is an element of F we have boolean AND(r)(i=1) F-i not equal theta or equivalently if F does not contain any m-triangle for m = 2, 3,..., r We prove that if n >= n(0)(r, k), then the r-wise intersecting family.. (F is an element of[([n])(k))]) containing the most number of (r + 1)-triangles is isomorphic to {F is an element of[([n])(k))) : vertical bar F n[r + 1]|>= r}.