In triangle ABC, let A′, B′ and C′ be points on the sides BC, CA and AB, respectively, such thatBA′A′C=CB′B′A=AC′C′B.The line parallel to B′C′ passing through A′ intersects line AC at P and line AB at Q. Prove thatPQB′C′⩾
Source: 2024 Argentina L3 P5
Tags: geometric inequality, inequalities, algebra, geometry
In triangle ABC, let A′, B′ and C′ be points on the sides BC, CA and AB, respectively, such thatBA′A′C=CB′B′A=AC′C′B.The line parallel to B′C′ passing through A′ intersects line AC at P and line AB at Q. Prove thatPQB′C′⩾