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<HKG = 90^o if AG = GH

Source: 2020 Balkan MO shortlist G2

September 14, 2021
geometryright angleBalkan MO Shortlistgeometry solvedBalkanEuler LineAngle Chasing

Problem Statement

Let G,HG, H be the centroid and orthocentre of △ABC\vartriangle ABC which has an obtuse angle at ∠B\angle B. Let ω\omega be the circle with diameter AGAG. ω\omega intersects ⊙(ABC)\odot(ABC) again at L≠AL \ne A. The tangent to ω\omega at LL intersects ⊙(ABC)\odot(ABC) at K≠LK \ne L. Given that AG=GHAG = GH, prove ∠HKG=90o\angle HKG = 90^o . Sam Bealing, United Kingdom
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