MathDB

9

Part of 1981 National High School Mathematics League

Problems(1)

Geometry Inequality

Source: 1981 National High School Mathematics League, Problem 9

2/20/2020
OO is a circle with a radius of 11, with strings CDCD and EFEF. CD//EFCD//EF, and diameter ABAB intersects CD,EFCD,EF at P,QP,Q. If ∠BPD=π4\angle BPD=\frac{\pi}{4}, prove that PC⋅QE+PD⋅QF<2.PC\cdot QE+PD \cdot QF<2.
geometryinequalities