Question

in triangle ABC angle A is acute, BD and CE are perpendicular on AC And AB prove that AB.AE=AC.AD

Answer 1

Step-by-step explanation:

Look at triangles AEC and ADB.  These share a common angle at A and the both have right angles (at E in the first and at D in the second).  So these two triangles are similar (by the AA rule).

Since triangle AEC is similar to triangle ADB, the ratios between corresponding sides are equal.  So

AE / AC = AD / AB

=> AB . AE = AC . AD