Grade 11 2023 Problem 5

GeometryLengthsOrthocenterTriangle

Dan je šiljastokutan trokut ABCABC s ortocentrom HH. Dokaži da vrijedi ∣AH∣2+∣BC∣2=∣BH∣2+∣CA∣2=∣CH∣2+∣AB∣2.|AH|^2 + |BC|^2 = |BH|^2 + |CA|^2 = |CH|^2 + |AB|^2.