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, \[\Delta ABC\sim \Delta DBA\sim \Delta DAC\] |
\[\frac{BC}{AB}=\frac{AC}{AD}\] |
\[\therefore \]\[BC\cdot AD=AB\cdot AC\] |
You need to login to perform this action.
You will be redirected in
3 sec