question_answer

ABC is a triangle right angled at A and a perpendicular AD is drawn on the hypotenuse BC. The value of \[BC\cdot AD\]is equal to

A) \[AB\cdot AC\]  

B) \[AB\cdot AD\]

C) \[CA\cdot CD\]              

D) \[AD\cdot DB\]

Correct Answer: A

Solution :

In case of a right angled triangle, if we draw a perpendicular from the vertex containing right angle to the hypotenuse, we get three triangles, two smaller and one original and these three triangles are similar triangles.

So,       \[\Delta ABC\sim \Delta DBA\sim \Delta DAC\]

\[\frac{BC}{AB}=\frac{AC}{AD}\]

\[\therefore \]\[BC\cdot AD=AB\cdot AC\]