MathDB

2

Part of 2000 Pan African

Problems(2)

Polynomial

Source: Pan African 2000

10/3/2005
Define the polynomials P0,P1,P2⋯P_0, P_1, P_2 \cdots by: P0(x)=x3+213x2−67x−2000 P_0(x)=x^3+213x^2-67x-2000 Pn(x)=Pn−1(x−n),n∈N P_n(x)=P_{n-1}(x-n), n \in N Find the coefficient of xx in P21(x)P_{21}(x).
algebrapolynomialquadratics
Circle and Tangent lines

Source: Pan African 2000

10/3/2005
Let γ\gamma be circle and let PP be a point outside γ\gamma. Let PAPA and PBPB be the tangents from PP to γ\gamma (where A,B∈γA, B \in \gamma). A line passing through PP intersects γ\gamma at points QQ and RR. Let SS be a point on γ\gamma such that BS∥QRBS \parallel QR. Prove that SASA bisects QRQR.
geometrytrigonometry