MathDB

3

Part of 1993 Irish Math Olympiad

Problems(2)

locus

Source: Ireland 1993

6/29/2009
A line l l is tangent to a circle S S at A A. For any points B,C B,C on l l on opposite sides of A A, let the other tangents from B B and C C to S S intersect at a point P P. If B,C B,C vary on l l so that the product AB⋅AC AB \cdot AC is constant, find the locus of P P.
geometry proposedgeometry
identity

Source: Ireland 1993

6/29/2009
If 1≤r≤n 1 \le r \le n are integers, prove the identity: \displaystyle\sum_{d\equal{}1}^{\infty}\binom {n\minus{}r\plus{}1}{d} \binom {r\minus{}1} {d\minus{}1}\equal{}\binom {n}{r}.
combinatorics unsolvedcombinatorics