in triangle ABC, angle A is acute , BD CE r perpendiculars onAC AB

prove that ABAE=ACAD

Question

in triangle ABC, angle A is acute , BD CE r perpendiculars onAC
AB
prove that AB*AE=AC*AD

Manbar Singh · Accepted Answer

In ∆AEC and ∆ADB,     ∠A = ∠A      common∠AEC = ∠ADB  90° each⇒∆AEC ~ ∆ADB AA⇒AEAD = ACAB = ECDB  Correponding sides of similar ∆'s are proportional⇒AEAD = ACAB⇒AE × AB = AC × AD

in triangle ABC, angle A is acute , BD CE r perpendiculars onAC AB prove that AB*AE=AC*AD

in triangle ABC, angle A is acute , BD CE r perpendiculars onAC AB

prove that ABAE=ACAD