1 Comment
In Triangle ABC, <ACB = 900 Þ <BCP = 900
So, In Triangle BPC: BC2 = BP2 – CP2 Now, In Triangle ABC, AB2 = AC2 + BC2 Þ AB2 = AC2 + BP2 – CP2 AB2 = AC2 – CP2 + BP2 AB2 = (AC - CP) (AC + CP) + BP2 AB2 = (AC - CP) (AP) + BP2 AB2 = (AC x AP - CP x AP) + BP2 AB2 = AC x AP + BP2 - CP x AP But, AP x CP = BP x PD (D APB ~ D CPB) AB2 = AC x AP + BP2 - BP x PD AB2 = AC x AP + BP(BP – PD) AB2 = AC x AP + BP x BD |