∫BC = BC’。
∴∠bc'c=∠bcc'; And < ∠a' c' b =∠ACB = 90°.
∴∠A'C'D=∠ACE (complementary angles of equal angles are equal)
∫A ' c ' = AC; ∠A ' DC ' =∠AEC = 90°。
∴⊿A'DC'≌⊿AEC(AAS),A'D=AE
So A'DP≌AEP can easily prove that P is the midpoint of AA'
Because the ratio of 30 degrees is CB/BA= 1/2.
C'BC is similar to A'BA, so C'C= 1/2A'A=AP.
The second question is the same, CB/BA= 1/ root 2.
C'C= 1/ root 2A'A= root 2AP