MathDB
Points, lines, circle

Source: Indonesia Mathematics Olympiad 2007 Day 2 Problem 7

June 2, 2008
geometrycircumcirclegeometry proposed

Problem Statement

Points A,B,C,D A,B,C,D are on circle S S, such that AB AB is the diameter of S S, but CD CD is not the diameter. Given also that C C and D D are on different sides of AB AB. The tangents of S S at C C and D D intersect at P P. Points Q Q and R R are the intersections of line AC AC with line BD BD and line AD AD with line BC BC, respectively. (a) Prove that P P, Q Q, and R R are collinear. (b) Prove that QR QR is perpendicular to line AB AB.
Back to ProblemsView on AoPS