Question

In a triangle ABC, CE is perpendicular to AB and BD to AC.. Prove AB x AE= AC x AD

Answer 1

quadrilateral  BEDC  is  a  cyclic  quadrilateral  and

and  AEB  and  ADC  are  two  secants  from  outside  point  A

hence  by  tangent  secant  therom,

AB X AE = AC X AD

Answer 2

Refer the attachment and...

Consider the △ABC,

So, we have to prove that, AB×AE=AC×AD

Now, consider the △ADB and △AEC,

∠A=∠A [common angle for both triangles]

∠ADB=∠AEC [both angles are equal to 90⁰]

△ADB∼△AEC

So, AB/AC=AD/AE

By cross multiplication we get,

AB×AE=AC×AD.