A) \[45{}^\circ \]
B) \[90{}^\circ \]
C) \[180{}^\circ \]
D) \[60{}^\circ \]
Correct Answer: B
Solution :
Given, \[\Delta ABC\] in which \[AD\bot \,BC\] and \[A{{D}^{2}}=BD\,.\,CD\]. |
Now, in \[\Delta DBA\] and \[\Delta DAC\], |
we have \[\angle BDA=\angle ADC=90{}^\circ\] |
\[\frac{BD}{AD}=\frac{AD}{CD}\] |
\[\Delta BDA=\Delta ADC=90{}^\circ \] [by SAS similarity] |
\[\angle B=\angle 2\] and \[\angle 1=\angle C\] |
\[\angle 1+\angle 2=\angle B+\angle C\] |
\[\angle A=\angle B+\angle C\] |
\[2\angle A=\angle A+\angle B+\angle C=180{}^\circ\] |
\[\angle A=\frac{180{}^\circ }{2}=90{}^\circ\] |
You need to login to perform this action.
You will be redirected in
3 sec