Question: prove that ab is perpendicular to bc?
Answer: In a triangle ABC, AD is perpendicular to BC, prove that AB^2+ CD^2 =AC^2+BD^2. ... AD^2+CD^2=AC^2. Subtracting these two equation we get BD^2-CD^2=AB^2-AC^2. Or rearranging we get AB^2+CD^2= AC^2+BD^2.