MathDB

2011.7

Part of Ukraine Correspondence MO - geometry

Problems(1)

AP _|_ BQ wanted, trapezoid with bases AB = 2CD, circle

Source: 2011 All-Ukrainain Correspondence MO of magazine ''In the World of Mathematics'', grades 5-12 p7

4/26/2021
Let ABCDABCD be a trapezoid in which AB∥CDAB \parallel CD and AB=2CDAB = 2CD. A line ℓ\ell perpendicular to CDCD was drawn through point CC. A circle with center at point DD and radius DADA intersects line ℓ\ell at points PP and QQ. Prove that AP⊥BQAP \perp BQ.
geometrytrapezoidperpendicularUkraine Correspondence