A) \[{{90}^{o}}\]
B) \[{{60}^{o}}\]
C) \[{{45}^{o}}\]
D) \[{{135}^{o}}\]
Correct Answer: A
Solution :
As shown in the figure, since P is the midpoint of AB and AB = 2AD, we have \[AB=2AP=2AD.\] or \[AP=AD.\] i.e., triangle ADP is an isosceles triangle. If \[\angle ADP=x\] and \[\angle APD=x,\]then, \[\angle A={{180}^{o}}-2x\] \[\Rightarrow \]\[\angle B=2x\] \[\angle CPB=\angle PCB={{90}^{o}}-x\] Since \[\angle APB={{180}^{o}}\]\[\angle DPC={{90}^{o}}\]
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