A) \[{{60}^{{}^\circ }}\]
B) \[{{75}^{{}^\circ }}\]
C) \[{{90}^{{}^\circ }}\]
D) \[{{45}^{{}^\circ }}\]
Correct Answer: C
Solution :
(c): In right angled \[\Delta ABD\] and \[\Delta ADC\], \[A{{B}^{2}}=A{{D}^{2}}+B{{D}^{2}}\] And, \[A{{C}^{2}}=A{{D}^{2}}+D{{C}^{2}}\] On adding, \[A{{B}^{2}}+A{{C}^{2}}=2A{{D}^{2}}+B{{D}^{2}}+C{{D}^{2}}\] \[\Rightarrow \]\[A{{B}^{2}}+A{{C}^{2}}=2BD\times CD+B{{D}^{2}}+C{{D}^{2}}\] \[\left[ \therefore A{{D}^{2}}=BD\times CD \right]\] \[\Rightarrow \]\[A{{B}^{2}}+A{{C}^{2}}={{\left( BD+CD \right)}^{2}}\] \[=B{{C}^{2}}\] \[\therefore \] \[\angle BAC={{90}^{{}^\circ }}\]
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