‌(x(c−b) ‌(x−a)⋅(c−b)=0 ‌AP⋅BC=0 ‌AP⟂BC ‌‌ and ‌x⋅(a−c)=a⋅b−b⋅c=(a−c)b ‌⇒(x−b)⋅(a−c)=0 ‌BP⋅AC=0 ‌∴‌‌BP⟂AC ∵ Point of intersection of altitude is called orthocentre. ∵P is orthocentre of △ABC.