MathDB
Equal segments

Source: China TST 2003

June 29, 2006
geometrycircumcircletrapezoidperpendicular bisectorgeometry unsolved

Problem Statement

Triangle ABCABC is inscribed in circle OO. Tangent PDPD is drawn from AA, DD is on ray BCBC, PP is on ray DADA. Line PUPU (UāˆˆBDU \in BD) intersects circle OO at QQ, TT, and intersect ABAB and ACAC at RR and SS respectively. Prove that if QR=STQR=ST, then PQ=UTPQ=UT.
Back to ProblemsView on AoPS